On local singularities in mathematical models of physical fields
Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Grinchenko, V. T. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1999 |
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| Schlagwörter: |
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| Anmerkung: |
© Kluwer Academic/Plenum Publishers 1999 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical sciences - Kluwer Academic Publishers-Plenum Publishers, 1994, 97(1999), 1 vom: Okt., Seite 3777-3795 |
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| Übergeordnetes Werk: |
volume:97 ; year:1999 ; number:1 ; month:10 ; pages:3777-3795 |
| Links: |
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| DOI / URN: |
10.1007/BF02364915 |
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| Katalog-ID: |
OLC2030756539 |
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| 520 | |a Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. | ||
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10.1007/BF02364915 doi (DE-627)OLC2030756539 (DE-He213)BF02364915-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Grinchenko, V. T. verfasserin aut On local singularities in mathematical models of physical fields 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. Boundary Condition Mathematical Model General Solution Singular Point Model Representation Ulitko, A. F. aut Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 97(1999), 1 vom: Okt., Seite 3777-3795 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:97 year:1999 number:1 month:10 pages:3777-3795 https://doi.org/10.1007/BF02364915 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 97 1999 1 10 3777-3795 |
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10.1007/BF02364915 doi (DE-627)OLC2030756539 (DE-He213)BF02364915-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Grinchenko, V. T. verfasserin aut On local singularities in mathematical models of physical fields 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. Boundary Condition Mathematical Model General Solution Singular Point Model Representation Ulitko, A. F. aut Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 97(1999), 1 vom: Okt., Seite 3777-3795 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:97 year:1999 number:1 month:10 pages:3777-3795 https://doi.org/10.1007/BF02364915 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 97 1999 1 10 3777-3795 |
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10.1007/BF02364915 doi (DE-627)OLC2030756539 (DE-He213)BF02364915-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Grinchenko, V. T. verfasserin aut On local singularities in mathematical models of physical fields 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. Boundary Condition Mathematical Model General Solution Singular Point Model Representation Ulitko, A. F. aut Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 97(1999), 1 vom: Okt., Seite 3777-3795 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:97 year:1999 number:1 month:10 pages:3777-3795 https://doi.org/10.1007/BF02364915 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 97 1999 1 10 3777-3795 |
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10.1007/BF02364915 doi (DE-627)OLC2030756539 (DE-He213)BF02364915-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Grinchenko, V. T. verfasserin aut On local singularities in mathematical models of physical fields 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. Boundary Condition Mathematical Model General Solution Singular Point Model Representation Ulitko, A. F. aut Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 97(1999), 1 vom: Okt., Seite 3777-3795 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:97 year:1999 number:1 month:10 pages:3777-3795 https://doi.org/10.1007/BF02364915 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 97 1999 1 10 3777-3795 |
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10.1007/BF02364915 doi (DE-627)OLC2030756539 (DE-He213)BF02364915-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Grinchenko, V. T. verfasserin aut On local singularities in mathematical models of physical fields 1999 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Kluwer Academic/Plenum Publishers 1999 Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. Boundary Condition Mathematical Model General Solution Singular Point Model Representation Ulitko, A. F. aut Enthalten in Journal of mathematical sciences Kluwer Academic Publishers-Plenum Publishers, 1994 97(1999), 1 vom: Okt., Seite 3777-3795 (DE-627)18219762X (DE-600)1185490-X (DE-576)038888130 1072-3374 nnns volume:97 year:1999 number:1 month:10 pages:3777-3795 https://doi.org/10.1007/BF02364915 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_22 GBV_ILN_40 GBV_ILN_70 GBV_ILN_2005 GBV_ILN_2088 GBV_ILN_4310 31.00 VZ AR 97 1999 1 10 3777-3795 |
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510 VZ 17,1 ssgn 31.00 bkl On local singularities in mathematical models of physical fields Boundary Condition Mathematical Model General Solution Singular Point Model Representation |
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On local singularities in mathematical models of physical fields |
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On local singularities in mathematical models of physical fields |
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Grinchenko, V. T. |
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Journal of mathematical sciences |
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Grinchenko, V. T. Ulitko, A. F. |
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on local singularities in mathematical models of physical fields |
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On local singularities in mathematical models of physical fields |
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Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. © Kluwer Academic/Plenum Publishers 1999 |
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Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. © Kluwer Academic/Plenum Publishers 1999 |
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Abstract In constructing mathematical models of physical fields there are various widely used hypotheses that include assumptions on the smoothness of the field, the nature of the boundary surfaces of the region of existence of the field and the properties of the interaction between the object being studied and surrounding objects. In many cases the use of convenient mathematical model representations leads to a situation in which some characteristics of the field do not have bounded values at individual points. The problem of the appearance of such local singularities in physical fields of different natures is of fundamental importance in the study of these fields by the methods of mathematical modeling, from the point of view of general understanding of the possibilities and content of mathematical modeling. The appearance of singularities in the characteristics of the field is a consequence of the contradictions arising when the properties of the medium and the nature of the boundary and the boundary conditions are modeled independently. In the present work we discuss a unified methodological approach to determining the nature of the singularity in various types of physical fields. The approach is based on introducing the concept of a general solution of the boundary-value problem and the use of such a solution in the vicinity of singular points. It is shown that the solutions with singularities give a reliable qualitative and quantitative description of the fields outside a small zone in a neighborhood of the singularity. Analysis of the solutions of boundary-value problems with local singularities shows the nature of the difficulties in interpreting the physical content of the solution near singularities. Typical situations are those in which interpenetration of different parts of the body is observed, the values of the displacements or velocities of certain points of the boundary depend on the direction of the limiting approach, and others. In a number of cases a priori knowledge of the nature of the singularity makes it possible to develop new approaches to the construction of effective solutions of boundary-value problems. © Kluwer Academic/Plenum Publishers 1999 |
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On local singularities in mathematical models of physical fields |
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