$L^p$--$L^q$ decay estimates for wave equations with monotone time-dependent dissipation

Michael Reissig; Jens Wirth

$L^p$--$L^q$ decay estimates for wave equations with monotone time-dependent dissipation

Analysis of PDEs 2008-10-27 v1

Authors: Michael Reissig , Jens Wirth

Abstract

This expository article is intended to give an overview about recently achieved results on asymptotic properties of solutions to the Cauchy problem $u_{tt}-\Delta u+b(t)u_t =0,\qquad u(0,\cdot)=u_1,\quad \mathrm{D}_tu(0,\cdot)=u_2$ for a wave equation with time-dependent dissipation term. The results are based on structural properties of the Fourier multipliers representing its solution. The article explains the general philosophy behind the approach.

Keywords

energy decay for wave equations cauchy problem parabolic equations

Cite

@article{arxiv.math/0508549,
  title  = {$L^p$--$L^q$ decay estimates for wave equations with monotone time-dependent dissipation},
  author = {Michael Reissig and Jens Wirth},
  journal= {arXiv preprint arXiv:math/0508549},
  year   = {2008}
}

Comments

15 pages, 2 figures

Related papers

View all related →