Energy Decay for Nonlinear Wave Equations with Degenerate Dissipative Terms

Mitsuhiro Nakao

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Abstract Decay rates of solutions of the initial-boundary value problem for nonlinear wave equations; utt−uxx+σ(x,ut)+β(x,u)=f(x,t)onI×R+u(x,0)=u0(x),ut(x,0)=u1(x)andu|∂I×R+=0 are derived, where I is a bounded interval in R and σ(x, v) is a function such that ∂∂vσ(x,v)≥0andσ(x,v)v≥a(x)|v|r+2 with r>-1, a(x)≥ 0 and 1/a(.)εLp(I) for some 0<p<∞.

Original languageEnglish
Pages (from-to)583-596
Number of pages14
JournalStudies in Mathematics and its Applications
Issue numberC
Publication statusPublished - 1986 Jan 1
Externally publishedYes



  • degenerate dissipative term
  • energy decay
  • energy method
  • nonlinear wave equation

ASJC Scopus subject areas

  • Applied Mathematics

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