Solution blow-up for a fractional in time acoustic wave equation

Mohamed Jleli, Mokhtar Kirane, Bessem Samet

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the fractional in time acoustic wave equation (Formula presented.) where 1<α<2, (Formula presented.) is the Caputo fractional derivative of order α, u=u(t,x), t>0, (Formula presented.), is the pressure in the medium, ε is the nonlinear acoustic parameter, ρ0 is the equilibrium density in the medium, and c0 is the equilibrium sound velocity. We study a Cauchy problem for this equation and a mixed boundary value problem in a bounded domain. For each problem, sufficient conditions for the blow-up of solutions are derived. Moreover, we provide a class of initial data for which there are no classical solutions even locally in time. Our approach is based on the nonlinear capacity method.

Original languageBritish English
Pages (from-to)6566-6575
Number of pages10
JournalMathematical Methods in the Applied Sciences
Volume43
Issue number10
DOIs
StatePublished - 15 Jul 2020

Keywords

  • blow-up
  • Caputo fractional derivative
  • fractional in time acoustic wave equation

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