Weakly coupled systems of quasilinear boundary value problem with applications to semilinear elliptic equations
type: Item
instance of: scholarly article
title: Weakly coupled systems of quasilinear boundary value problem with applications to semilinear elliptic equations
zbMATH Open document ID: 0879.35093
published in: Differential and Integral Equations
publication date: 1997-12-10T00:00:00Z
review text: The authors develop a qualitative theory of diagonal quasilinear hyperbolic systems of the form \(\partial_t u_i + \partial_x f_i(u_i) = g_i(U)\), \(i=1, \dots ,N\), \(U = (u_1, \dots ,u_N)\), with locally Lipschitz continuous functions \(f_1, \dots ,f_N\), \(g_1, \dots , g_N\). They establish local existence and continuation properties for Kruzhkov-type entropy solutions of the Cauchy problem and use the concept of quasi-monotonicity of the mapping \(G=(g_1, \dots ,g_N)\) for proving comparison theorems for entropy sub- and supersolutions. The general results are then applied to concrete problems arising in chromatography, combustion theory and nonlinear optics.
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1095813
zbMATH Keywords: conservation laws
zbMATH Keywords: entropy solutions
zbMATH Keywords: comparison theorems
author: Roberto Natalini
author: Bernard Hanouzet
reviewed by: Pavel Krejč{í }
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1095813