๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Nonexistence of Global Solutions of Some Quasilinear Hyperbolic Equations

โœ Scribed by Mehmet Can; Sang Ro Park; Fahreddin Aliyev

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
194 KB
Volume
213
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

โœฆ Synopsis

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 one writes down a functional which reflects the properties of dissipative boundary conditions and represents the norm of the solution in some sense. Then it is proved that this functional satisfies the hypotheses of the concavity lemma. Hence from the conclusion of the lemma one concludes that this functional and hence the norm of the solution blows up in a finite time.

๐Ÿ“œ SIMILAR VOLUMES

Nonexistence of Global Solutions of Some
Nonexistence of Global Solutions of Some Quasilinear Hyperbolic Equations with Dynamic Boundary Conditions
โœ M. Kirane; S. Kouachi; N. Tatar ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 266 KB

In this paper the non-existence of global solutions of two fourth-order hyperbolic equations with dynamic boundary conditions is considered. The method of proof makes use of the generalized convexity method due to LADYZHENSKAYA and KALANTAROV [4].

Wavelet-Galerkin solutions of quasilinea
Wavelet-Galerkin solutions of quasilinear hyperbolic conservation equations
โœ Avudainayagam, A. ;Vani, C. ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 172 KB ๐Ÿ‘ 2 views

The compactly supported orthogonal wavelet bases developed by Daubechies are used in the Galerkin scheme for a class of one-dimensional ยฎrst-order quasilinear conservation equations with perturbed dissipative terms. We ยฎrst develop a recursive algorithm to obtain the wavelet coecients of a dissipati

Asymptotic behaviour of global classical
Asymptotic behaviour of global classical solutions of diagonalizable quasilinear hyperbolic systems
โœ Jianli Liu; Yi Zhou ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 176 KB

## 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,