Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit
Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic i...
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| Autor*in: |
Tóth, Bálint [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2005 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2005 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer-Verlag, 1965, 256(2005), 1 vom: 08. März, Seite 111-157 |
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| Übergeordnetes Werk: |
volume:256 ; year:2005 ; number:1 ; day:08 ; month:03 ; pages:111-157 |
| Links: |
|---|
| DOI / URN: |
10.1007/s00220-005-1314-9 |
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| Katalog-ID: |
OLC2038886644 |
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| 520 | |a Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. | ||
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10.1007/s00220-005-1314-9 doi (DE-627)OLC2038886644 (DE-He213)s00220-005-1314-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Tóth, Bálint verfasserin aut Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. Entropy Smooth Solution Relative Entropy Entropy Method Hydrodynamic Limit Valkó, Benedek aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 256(2005), 1 vom: 08. März, Seite 111-157 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:256 year:2005 number:1 day:08 month:03 pages:111-157 https://doi.org/10.1007/s00220-005-1314-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 256 2005 1 08 03 111-157 |
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10.1007/s00220-005-1314-9 doi (DE-627)OLC2038886644 (DE-He213)s00220-005-1314-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Tóth, Bálint verfasserin aut Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. Entropy Smooth Solution Relative Entropy Entropy Method Hydrodynamic Limit Valkó, Benedek aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 256(2005), 1 vom: 08. März, Seite 111-157 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:256 year:2005 number:1 day:08 month:03 pages:111-157 https://doi.org/10.1007/s00220-005-1314-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 256 2005 1 08 03 111-157 |
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10.1007/s00220-005-1314-9 doi (DE-627)OLC2038886644 (DE-He213)s00220-005-1314-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Tóth, Bálint verfasserin aut Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. Entropy Smooth Solution Relative Entropy Entropy Method Hydrodynamic Limit Valkó, Benedek aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 256(2005), 1 vom: 08. März, Seite 111-157 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:256 year:2005 number:1 day:08 month:03 pages:111-157 https://doi.org/10.1007/s00220-005-1314-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 256 2005 1 08 03 111-157 |
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10.1007/s00220-005-1314-9 doi (DE-627)OLC2038886644 (DE-He213)s00220-005-1314-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Tóth, Bálint verfasserin aut Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. Entropy Smooth Solution Relative Entropy Entropy Method Hydrodynamic Limit Valkó, Benedek aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 256(2005), 1 vom: 08. März, Seite 111-157 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:256 year:2005 number:1 day:08 month:03 pages:111-157 https://doi.org/10.1007/s00220-005-1314-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 256 2005 1 08 03 111-157 |
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10.1007/s00220-005-1314-9 doi (DE-627)OLC2038886644 (DE-He213)s00220-005-1314-9-p DE-627 ger DE-627 rakwb eng 530 510 VZ Tóth, Bálint verfasserin aut Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit 2005 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2005 Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. Entropy Smooth Solution Relative Entropy Entropy Method Hydrodynamic Limit Valkó, Benedek aut Enthalten in Communications in mathematical physics Springer-Verlag, 1965 256(2005), 1 vom: 08. März, Seite 111-157 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:256 year:2005 number:1 day:08 month:03 pages:111-157 https://doi.org/10.1007/s00220-005-1314-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_22 GBV_ILN_24 GBV_ILN_30 GBV_ILN_40 GBV_ILN_70 GBV_ILN_120 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2010 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4116 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4317 GBV_ILN_4318 GBV_ILN_4319 AR 256 2005 1 08 03 111-157 |
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Enthalten in Communications in mathematical physics 256(2005), 1 vom: 08. März, Seite 111-157 volume:256 year:2005 number:1 day:08 month:03 pages:111-157 |
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perturbation of singular equilibria of hyperbolic two-component systems: a universal hydrodynamic limit |
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Perturbation of Singular Equilibria of Hyperbolic Two-Component Systems: A Universal Hydrodynamic Limit |
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Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. © Springer-Verlag Berlin Heidelberg 2005 |
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Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. © Springer-Verlag Berlin Heidelberg 2005 |
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Abstract We consider one-dimensional, locally finite interacting particle systems with two conservation laws which under the Eulerian hydrodynamic limit lead to two-by-two systems of conservation laws: with where is a convex compact polygon in $ ℝ^{2} $. The system is typically strictly hyperbolic in the interior of with possible non-hyperbolic degeneracies on the boundary ∂. We consider the case of an isolated singular (i.e. non-hyperbolic) point on the interior of one of the edges of , call it (ρ0,u0). We investigate the propagation of small nonequilibrium perturbations of the steady state of the microscopic interacting particle system, corresponding to the densities (ρ0,u0) of the conserved quantities. We prove that for a very rich class of systems, under a proper hydrodynamic limit the propagation of these small perturbations are universally driven by the two-by-two system where the parameter γ is the only trace of the microscopic structure. The proof relies on the relative entropy method and thus, it is valid only in the regime of smooth solutions of the pde. But there are essential new elements: in order to control the fluctuations of the terms with Poissonian (rather than Gaussian) decay coming from the low density approximations we have to apply refined pde estimates. In particular Lax entropies of these pde systems play a not merely technical key role in the main part of the proof. © Springer-Verlag Berlin Heidelberg 2005 |
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