𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems

✍ Scribed by Jianli Liu; Yi Zhou

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
176 KB
Volume
30
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper is concerned with the asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems with linearly degenerate characteristic fields. Based on the existence results of global classical solutions, we prove that when t tends to infinity, the solution approaches a combination of C^1^ travelling wave solutions, provided that L^1^ ∩ L^∞^ norm of the initial data as well as its derivative are bounded. Application is given for the time‐like extremal surface in Minkowski space. Copyright Β© 2006 John Wiley & Sons, Ltd.

πŸ“œ SIMILAR VOLUMES

Point-wise decay estimate for the global
Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems
✍ Yi Zhou πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 102 KB

## Abstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (__Commun. Partial Differential Equations__ 1994; **19**:1263–1317

Nonexistence of Global Solutions of Some
Nonexistence of Global Solutions of Some Quasilinear Hyperbolic Equations
✍ Mehmet Can; Sang Ro Park; Fahreddin Aliyev πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 194 KB

In this work, the nonexistence of the global solutions to initial boundary value problems with dissipative terms in the boundary conditions is considered for a class of quasilinear hyperbolic equations. The nonexistence proof is achieved by the usage of the so-called concavity method. In this method