Stability of degenerate stationary waves for viscous gases
type: Item
instance of: scholarly article
title: Stability of degenerate stationary waves for viscous gases
zbMATH Open document ID: 1228.76060
author: Yoshihiro Ueda
author: Tohru Nakamura
author: Shuichi Kawashima
published in: Archive for Rational Mechanics and Analysis
publication date: 2011-09-27T00:00:00Z
review text: The Dirichlet-Cauchy problem for second order partial differential equations of the type, the parabolic \(u_t+f(u)_x=\mu u_{ xx}\) or the hyperbolic \( u_{ tt}+u_t+f(u)_x= u_{ xx}\), in \((\mathbb R^+)^2\) admit solutions that convergent to a stationary wave, provided by some smooth convex function \(f=f(u)\) conveniently chosen, \(\mu>0\) and \(u_b<u_+=\lim_{x\rightarrow \infty}u_0(x)\), with \(u_b\) and \(u_0\) representing respectively a constant boundary value and an initial function. The \(L^p\)-stability analysis is based on the space-time weighted energy method.
reviewed by: Luisa Consiglieri
Mathematics Subject Classification ID: 76E30
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 5951199
zbMATH Keywords: asymptotic stability
zbMATH Keywords: weighted energy method
MaRDI profile type: Publication
full work available at URL: s00205-010-0369-8
OpenAlex ID: W2017888000
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DOI: 10.1007/S00205-010-0369-8
description: scientific article; zbMATH DE number 5951199