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Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms

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  • Xuhui Shen
  • Dandan Wu
  • Genni Fragnelli

Abstract

This paper considers the blow-up phenomena for the following reaction-diffusion problem with nonlocal and gradient terms: ut=Δum+∫Ωurdx−∇us,in Ω×0,t∗,∂u/∂ν=gu,on  ∂Ω  ×0,t∗,ux,0=u0x≥0,in Ω¯. Here m>1, and Ω⊂℠NN≥2 is a bounded and convex domain with smooth boundary. Applying a Sobolev inequality and a differential inequality technique, lower bounds for blow-up time when blow-up occurs are given. Moreover, two examples are given as applications to illustrate the abstract results obtained in this paper.

Suggested Citation

  • Xuhui Shen & Dandan Wu & Genni Fragnelli, 2022. "Blow-Up Phenomena in Reaction-Diffusion Problems with Nonlocal and Gradient Terms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2022, pages 1-12, April.
    • Handle: RePEc:hin:jnddns:8364982
    DOI: 10.1155/2022/8364982
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