Description

• Title:
  Asymptotic behavior of solutions of some nonlinearly damped wave equations on $\mathbb R^N$
• Creator:
  Karachalios, Nikos;
  Stavrakakis, Nikos M.
• Description:
  We discuss the asymptotic behavior of solutions of the nonlinearly damped wave equation $$ u_{tt} +\delta \vert u_t\vert ^{m-1}u_t -\phi (x)\Delta u = \lambda u\vert u\vert ^{\beta -1}, \quad x \in \mathbb R^n, \ t \geq 0, $$ with the initial conditions $ u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N \geq 3$, $ \delta > 0$ and $(\phi (x))^{-1} =g (x)$ is a positive function lying in $L^{p}(\mathbb R^n)\cap L^{\infty}(\mathbb R^n)$, for some $p$. We prove blow-up of solutions when the source term dominates over the damping, and the initial energy is assumed to be positive. We also discuss global existence energy decay of solutions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2001.09.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 18, No 1 (September 2001); 73 - 87;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.024/9936
• Subject:
  Semilinear hyperbolic equations;
  blow-up;
  nonlinear dissipation;
  potential well;
  concavity method;
  unbounded domains;
  generalized Sobolev spaces;
  Primary 35L15;
  35L70;
  35L80;
  Secondary 35A07;
  35B40;
  35B45;
  47F05;
  47H20
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.024
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other