Non-existence of global solutions to systems of non-autonomous nonlinear parabolic equations

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We consider the non-autonomous system of nonlinear parabolic equations { ut+ trΔαu = vq v t + tsΔβv=up posed in Q := (0, ∞) × RN, subject to the initial data (u(0,x) = u0(x), v(0, x) = vo(x)), where p > 1 and q > 1 are positive real numbers, α, β €]0,2] and Δγ := (-Δ)γ/2 is the (-Δ)γ/2 fractional power of -Δ in the x variable defined via the Fourier transform and its inverse -1 by (-Δ)γ/2ω(x,t) = -1 (vγ(ω) (ξ)) (x,t), where r > -1 and s > -1. The Fujita critical exponent which separates the case of blowing-up solutions from the case of globally in time existing solutions is determined.

Original languageEnglish
Pages (from-to)203-212
Number of pages10
JournalCommunications in Applied Analysis
Issue number2
Publication statusPublished - Apr 2010



  • Critical exponent
  • Non-autonomous reaction-diffusion systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Modelling and Simulation
  • Numerical Analysis

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