Large time behavior of solutions to a semilinear hyperbolic system with relatxaion

Yoshihiro Ueda, Shuichi Kawashima

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8 Citations (Scopus)

Abstract

We are concerned with the initial value problem for a damped wave equation with a nonlinear convection term which is derived from a semilinear hyperbolic system with relaxation. We show the global existence and asymptotic decay of solutions in W1,p (1 ≤ p ≤ ∞) under smallness condition on the initial data. Moreover, we show that the solution approaches in W1,p (1 ≤ p ≤ ∞) the nonlinear diffusion wave expressed in terms of the self-similar solution of the Burgers equation as time tends to infinity. Our results are based on the detailed pointwise estimates for the fundamental solutions to the linearlized equation.

Original languageEnglish
Pages (from-to)147-179
Number of pages33
JournalJournal of Hyperbolic Differential Equations
Volume4
Issue number1
Publication statusPublished - Mar 2007

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Analysis

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