Convergence of a blow-up curve for a semilinear wave equation

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Abstract

We consider a blow-up phenomenon for ∂t2uε −ε2x2uε = F(∂tuε). The derivative of the solution ∂tuε blows-up on a curve t = Tε(x) if we impose some conditions on the initial values and the nonlinear term F. We call Tε blow-up curve for ∂t2uε −ε2x2uε = F(∂tuε). In the same way, we consider the blow-up curve t = T-(x) for ∂t2u = F(∂tu). The purpose of this paper is to show that, for each x, Tε(x) converges to T-(x) as ε → 0.

Original languageEnglish
Pages (from-to)1133-1143
Number of pages11
JournalDiscrete and Continuous Dynamical Systems - Series S
Volume14
Issue number3
DOIs
Publication statusPublished - 2021 Mar
Externally publishedYes

Keywords

  • Blow-up
  • Numerical analysis
  • Wave equation

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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