Nonexistence of global solutions to a hyperbolic equation with a space-time fractional damping

M. Kirane, Y. Laskri

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We establish conditions that ensure the absence of global solutions to the nonlinear hyperbolic equation with a time-space fractional damping:utt-Δu+(-Δ)β/2D+αu=|u|p,where (-Δ) β/2, 1 ≤ β ≤ 2 stands for the β/2 fractional power of the Laplacien and D+α is the Riemann-Liouville's time fractional derivative [10]. Our results include nonexistence results as well as necessary conditions for the local and global solvability. The method used is based on a duality argument with an appropriate choice of the test function and a scaling argument.

Original languageBritish English
Pages (from-to)1304-1310
Number of pages7
JournalApplied Mathematics and Computation
Volume167
Issue number2
DOIs
StatePublished - 15 Aug 2005

Keywords

  • Hyperbolic equation
  • Nonexistence
  • Space-time fractional damping

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