Rarefactions and large time behavior for parabolic equations and monotone schemes
type: Item
instance of: scholarly article
title: Rarefactions and large time behavior for parabolic equations and monotone schemes
zbMATH Open document ID: 0645.65052
DOI: 10.1007/BF01229452
author: Eduard Harabetian
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: Solutions of the degenerate parabolic equation \(u_ t+f(u)_ x=A(u)_{xx}\) and of the associated difference equation \[ u^{n+1}(x)- u^ n(x)=-\lambda \Delta_ d(g(u^ n(x-p_ 0d),...,u^ n(x+q_ 0d)) \] are approximated for large t by those of \(u_ t+f(u)_ x=0\). Here u is scalar, f is convex and A'(u)\(\geq 0\). For \(A(u)=| u|^{\gamma}u\) we have the porous medium equation and for \(f(u)=0,5u^ 2\), \(A(u)=u\) we get Burger's equation. An asymptotic convergence rate is also given.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 4052921
zbMATH Keywords: rarefactions
zbMATH Keywords: large time behavior
zbMATH Keywords: monotone schemes
zbMATH Keywords: degenerate parabolic equation
zbMATH Keywords: difference equation
zbMATH Keywords: porous medium equation
zbMATH Keywords: Burger's equation
zbMATH Keywords: asymptotic convergence rate
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4052921