Relative entropy in diffusive relaxation

Corrado Lattanzio; Athanasios E. Tzavaras

doi:10.1137/120891307

Relative entropy in diffusive relaxation

Corrado Lattanzio, Athanasios E. Tzavaras

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

Abstract

We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate type.

Original language	English (US)
Pages (from-to)	1563-1584
Number of pages	22
Journal	SIAM Journal on Mathematical Analysis
Volume	45
Issue number	3
DOIs	https://doi.org/10.1137/120891307
State	Published - 2013
Externally published	Yes

Keywords

Diffusive relaxation
Euler equations
Relative entropy

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/120891307

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title = "Relative entropy in diffusive relaxation",

abstract = "We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate type.",

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author = "Corrado Lattanzio and Tzavaras, {Athanasios E.}",

year = "2013",

doi = "10.1137/120891307",

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volume = "45",

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T1 - Relative entropy in diffusive relaxation

AU - Lattanzio, Corrado

AU - Tzavaras, Athanasios E.

PY - 2013

Y1 - 2013

N2 - We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate type.

AB - We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum. The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy. The relative entropy method is also employed to establish convergence from entropic weak solutions of viscoelasticity with memory to the system of viscoelasticity of the rate type.

KW - Diffusive relaxation

KW - Euler equations

KW - Relative entropy

UR - http://www.scopus.com/inward/record.url?scp=84884756213&partnerID=8YFLogxK

U2 - 10.1137/120891307

DO - 10.1137/120891307

M3 - Article

AN - SCOPUS:84884756213

SN - 0036-1410

VL - 45

SP - 1563

EP - 1584

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 3

ER -

Relative entropy in diffusive relaxation

Abstract

Keywords

ASJC Scopus subject areas

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