Title of article :
Long-time behavior of solutions to a nonlinear hyperbolic relaxation system
Author/Authors :
Rafael Orive، نويسنده , , Enrique Zuazua، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2006
Abstract :
We study the large time behavior of solutions of a one-dimensional hyperbolic relaxation system that may be written as a nonlinear damped wave equation. First, we prove the global existence of a unique solution and their decay properties for sufficiently small initial data. We also show that for some large initial data, solutions blow-up in finite time. For quadratic nonlinearities, we prove that the large time behavior of solutions is given by the fundamental solution of the viscous Burgers equation. In some other cases, the convection term is too weak and the large time behavior is given by the linear heat kernel.
Keywords :
Hyperbolic relaxation system , damped wave equation , Asymptotic behavior , Convective heat equation , Blow-up
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS
Journal title :
JOURNAL OF DIFFERENTIAL EQUATIONS