Global nonexistence for the cauchy problem of some nonlinear reaction-diffusion systems

Mokhtar Kirane, Mahmoud Qafsaoui

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

Abstract

We, first, consider the parabolic equation ut = -(-Δ)α/2um + a(x).∇uq + f(t, x)u'p + w(t, x), t > 0, x ∈ ℝN, where (-Δ)α/2 is the α/2-fractional power of the Laplacian - Δ which for 0 < α ≤ 2 stands for impurities and f(t, x) and w(t, x) are given nonnegative functions, and find its critical exponent. Then, we consider the criticality for five systems of strongly coupled parabolic equations, two of them with nonlinear convective terms. Our results answer positively some open problems raised recently by Bandle, Deng, Levine, and Zhang.

Original languageBritish English
Pages (from-to)217-243
Number of pages27
JournalJournal of Mathematical Analysis and Applications
Volume268
Issue number1
DOIs
StatePublished - 1 Apr 2002

Keywords

  • Blow-up
  • Degenerate systems
  • Fractal diffusion operator
  • Nonlinear reaction-diffusion systems
  • Porous media
  • Strongly coupled systems

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