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Type: Artigo
Title: Approximation of entropy solutions to degenerate nonlinear parabolic equations
Author: Abreu, Eduardo
Colombeau, Mathilde
Panov, Evgeny YU
Abstract: We approximate the unique entropy solutions to general multidimensional degenerate parabolic equations with BV continuous flux and continuous nondecreasing diffusion function (including scalar conservation laws with BV continuous flux) in the periodic case. The approximation procedure reduces, by means of specific formulas, a system of PDEs to a family of systems of the same number of ODEs in the Banach space L∞, whose solutions constitute a weak asymptotic solution of the original system of PDEs. We establish well posedness, monotonicity and L1-stability. We prove that the sequence of approximate solutions is strongly L1-precompact and that it converges to an entropy solution of the original equation in the sense of Carrillo. This result contributes to justify the use of this original method for the Cauchy problem to standard multidimensional systems of fluid dynamics for which a uniqueness result is lacking
Subject: Equações diferenciais parciais - Teoria assintótica
Equações diferenciais parabólicas
Problema de
Partial differential equations - Asymptotic theory
Hyperbolic differential equations
Cauchy problem
Country: Suiça
Editor: Springer
Rights: fechado
Identifier DOI: 10.1007/s00033-017-0877-6
Date Issue: 2017
Appears in Collections:IMECC - Artigos e Outros Documentos

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