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Blow-up and global existence for semilinear parabolic systems with space-time forcing terms

Author

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  • Fino, Ahmad Z.
  • Jleli, Mohamed
  • Samet, Bessem

Abstract

We investigate the finite time blow-up and global existence of sign-changing solutions to the Cauchy problem for the inhomogeneous semilinear parabolic system with space-time forcing terms{ut−Δu=|v|p+tσw1(x),x∈RN,t>0,vt−Δv=|u|q+tγw2(x),x∈RN,t>0,(u(0,x),v(0,x))=(u0(x),v0(x)),x∈RN,where N≥1,p,q>1,σ,γ>−1,σ,γ≠0,w1,w2≢0, and u0,v0∈C0(RN). For the finite time blow-up, two cases are discussed under the conditions wi∈L1(RN) and ∫RNwi(x)dx>0,i=1,2. Namely, if σ>0 or γ>0, we show that the (mild) solution (u,v) to the considered system blows up in finite time, while if σ,γ∈(−1,0), then a finite time blow-up occurs when N2σγ and q>γσ, we show that the solution is global for suitable initial values and wi,i=1,2.

Suggested Citation

  • Fino, Ahmad Z. & Jleli, Mohamed & Samet, Bessem, 2021. "Blow-up and global existence for semilinear parabolic systems with space-time forcing terms," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
  • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003362
    DOI: 10.1016/j.chaos.2021.110982
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    Cited by:

    1. Zhao, Yongqiang & Tang, Yanbin, 2024. "Critical behavior of a semilinear time fractional diffusion equation with forcing term depending on time and space," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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