Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems
type: Item
instance of: scholarly article
title: Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems
zbMATH Open document ID: 0584.35068
author: Tiehu Qin
published in: Chinese Annals of Mathematics. Series B
publication date: 1985-01-01T00:00:00Z
review text: The author considers initial-boundary value problems for first order quasilinear hyperbolic systems and discusses the existence of global smooth solutions and the exponential decay of the solutions in \(C^ 1\)- space. Assuming a condition which is almost equivalent to the strict hyperbolicity, he gets a system of ordinary differential equations obtained along characteristic curves. Here he puts a condition on the boundary conditions which expresses the dissipative effect on the boundary, i.e., which guarantees the existence of global solutions for the above system of ordinary differential equations. Using this result, he obtains the global smooth solutions of the hyperbolic systems.
Mathematics Subject Classification ID: 35L50
Mathematics Subject Classification ID: 35L45
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 3935612
zbMATH Keywords: initial-boundary value problems
zbMATH Keywords: first order quasilinear hyperbolic systems
zbMATH Keywords: characteristic curves
zbMATH Keywords: dissipative effect
reviewed by: Mikio Tsuji
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3935612