An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions

Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which...
Ausführliche Beschreibung

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Autor*in:	Casado-Díaz, Juan [verfasserIn] Maestre, Faustino

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Elliptic equation Wave equation Unbounded domain Thin domain Corrector

Anmerkung:	© Universidad Complutense de Madrid 2019

Übergeordnetes Werk:	Enthalten in: Revista matemática complutense - Madrid : Univ., 1988, 32(2019), 3 vom: 09. März, Seite 681-730
Übergeordnetes Werk:	volume:32 ; year:2019 ; number:3 ; day:09 ; month:03 ; pages:681-730

Links:	Volltext

DOI / URN:	10.1007/s13163-019-00299-x

Katalog-ID:	SPR030714923

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520			\|a Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam.
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publishDate	2019
allfields	10.1007/s13163-019-00299-x doi (DE-627)SPR030714923 (SPR)s13163-019-00299-x-e DE-627 ger DE-627 rakwb eng Casado-Díaz, Juan verfasserin (orcid)0000-0001-5122-7449 aut An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universidad Complutense de Madrid 2019 Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. Elliptic equation (dpeaa)DE-He213 Wave equation (dpeaa)DE-He213 Unbounded domain (dpeaa)DE-He213 Thin domain (dpeaa)DE-He213 Corrector (dpeaa)DE-He213 Maestre, Faustino (orcid)0000-0001-6644-0277 aut Enthalten in Revista matemática complutense Madrid : Univ., 1988 32(2019), 3 vom: 09. März, Seite 681-730 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:32 year:2019 number:3 day:09 month:03 pages:681-730 https://dx.doi.org/10.1007/s13163-019-00299-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 32 2019 3 09 03 681-730
spelling	10.1007/s13163-019-00299-x doi (DE-627)SPR030714923 (SPR)s13163-019-00299-x-e DE-627 ger DE-627 rakwb eng Casado-Díaz, Juan verfasserin (orcid)0000-0001-5122-7449 aut An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universidad Complutense de Madrid 2019 Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. Elliptic equation (dpeaa)DE-He213 Wave equation (dpeaa)DE-He213 Unbounded domain (dpeaa)DE-He213 Thin domain (dpeaa)DE-He213 Corrector (dpeaa)DE-He213 Maestre, Faustino (orcid)0000-0001-6644-0277 aut Enthalten in Revista matemática complutense Madrid : Univ., 1988 32(2019), 3 vom: 09. März, Seite 681-730 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:32 year:2019 number:3 day:09 month:03 pages:681-730 https://dx.doi.org/10.1007/s13163-019-00299-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 32 2019 3 09 03 681-730
allfields_unstemmed	10.1007/s13163-019-00299-x doi (DE-627)SPR030714923 (SPR)s13163-019-00299-x-e DE-627 ger DE-627 rakwb eng Casado-Díaz, Juan verfasserin (orcid)0000-0001-5122-7449 aut An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universidad Complutense de Madrid 2019 Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. Elliptic equation (dpeaa)DE-He213 Wave equation (dpeaa)DE-He213 Unbounded domain (dpeaa)DE-He213 Thin domain (dpeaa)DE-He213 Corrector (dpeaa)DE-He213 Maestre, Faustino (orcid)0000-0001-6644-0277 aut Enthalten in Revista matemática complutense Madrid : Univ., 1988 32(2019), 3 vom: 09. März, Seite 681-730 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:32 year:2019 number:3 day:09 month:03 pages:681-730 https://dx.doi.org/10.1007/s13163-019-00299-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 32 2019 3 09 03 681-730
allfieldsGer	10.1007/s13163-019-00299-x doi (DE-627)SPR030714923 (SPR)s13163-019-00299-x-e DE-627 ger DE-627 rakwb eng Casado-Díaz, Juan verfasserin (orcid)0000-0001-5122-7449 aut An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universidad Complutense de Madrid 2019 Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. Elliptic equation (dpeaa)DE-He213 Wave equation (dpeaa)DE-He213 Unbounded domain (dpeaa)DE-He213 Thin domain (dpeaa)DE-He213 Corrector (dpeaa)DE-He213 Maestre, Faustino (orcid)0000-0001-6644-0277 aut Enthalten in Revista matemática complutense Madrid : Univ., 1988 32(2019), 3 vom: 09. März, Seite 681-730 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:32 year:2019 number:3 day:09 month:03 pages:681-730 https://dx.doi.org/10.1007/s13163-019-00299-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 32 2019 3 09 03 681-730
allfieldsSound	10.1007/s13163-019-00299-x doi (DE-627)SPR030714923 (SPR)s13163-019-00299-x-e DE-627 ger DE-627 rakwb eng Casado-Díaz, Juan verfasserin (orcid)0000-0001-5122-7449 aut An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Universidad Complutense de Madrid 2019 Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. Elliptic equation (dpeaa)DE-He213 Wave equation (dpeaa)DE-He213 Unbounded domain (dpeaa)DE-He213 Thin domain (dpeaa)DE-He213 Corrector (dpeaa)DE-He213 Maestre, Faustino (orcid)0000-0001-6644-0277 aut Enthalten in Revista matemática complutense Madrid : Univ., 1988 32(2019), 3 vom: 09. März, Seite 681-730 (DE-627)327098120 (DE-600)2043797-3 1988-2807 nnns volume:32 year:2019 number:3 day:09 month:03 pages:681-730 https://dx.doi.org/10.1007/s13163-019-00299-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 32 2019 3 09 03 681-730
language	English
source	Enthalten in Revista matemática complutense 32(2019), 3 vom: 09. März, Seite 681-730 volume:32 year:2019 number:3 day:09 month:03 pages:681-730
sourceStr	Enthalten in Revista matemática complutense 32(2019), 3 vom: 09. März, Seite 681-730 volume:32 year:2019 number:3 day:09 month:03 pages:681-730
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Elliptic equation Wave equation Unbounded domain Thin domain Corrector
isfreeaccess_bool	false
container_title	Revista matemática complutense
authorswithroles_txt_mv	Casado-Díaz, Juan @@aut@@ Maestre, Faustino @@aut@@
publishDateDaySort_date	2019-03-09T00:00:00Z
hierarchy_top_id	327098120
id	SPR030714923
language_de	englisch
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author	Casado-Díaz, Juan
spellingShingle	Casado-Díaz, Juan misc Elliptic equation misc Wave equation misc Unbounded domain misc Thin domain misc Corrector An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions
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topic_title	An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions Elliptic equation (dpeaa)DE-He213 Wave equation (dpeaa)DE-He213 Unbounded domain (dpeaa)DE-He213 Thin domain (dpeaa)DE-He213 Corrector (dpeaa)DE-He213
topic	misc Elliptic equation misc Wave equation misc Unbounded domain misc Thin domain misc Corrector
topic_unstemmed	misc Elliptic equation misc Wave equation misc Unbounded domain misc Thin domain misc Corrector
topic_browse	misc Elliptic equation misc Wave equation misc Unbounded domain misc Thin domain misc Corrector
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title	An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions
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title_full	An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions
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title_sort	elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions
title_auth	An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions
abstract	Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. © Universidad Complutense de Madrid 2019
abstractGer	Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. © Universidad Complutense de Madrid 2019
abstract_unstemmed	Abstract The paper is divided in two parts. In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. Here, we show that the boundary conditions also produce almost periodic oscillations in the direction of the axis of the beam. © Universidad Complutense de Madrid 2019
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title_short	An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions
url	https://dx.doi.org/10.1007/s13163-019-00299-x
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doi_str	10.1007/s13163-019-00299-x
up_date	2024-07-03T19:42:34.171Z
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In the first one, we consider a linear elliptic partial differential equation, or system, in an unbounded cylinder with a nonpositive term of zero order. We analyze the existence and the dimension of the space of solutions, when we look for solutions which tend exponentially to zero at infinity and for oscillatory solutions which have a potential growth at infinity. This type of problems appears when we study the influence of boundary conditions in homogenization, singular perturbation problems and reduction of dimension problems. As an example, we obtain a corrector result for a wave problem in a thin beam imposing initial and boundary conditions. It was known that the initial conditions produce almost periodic oscillations in time. 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An elliptic equation in an unbounded cylinder: applications to the behavior of a wave in a thin beam with boundary conditions

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