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Blow-Up Analysis for a Reaction-Diffusion Model with Nonlocal and Gradient Terms

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  • Xuhui Shen
  • Lun Lan
  • Julien Bruchon

Abstract

In this paper, we investigate the blow-up phenomena for the following reaction-diffusion model with nonlocal and gradient terms: ut=Δu+aup∫Ωuαdxm−∇uqin Ω×0,t∗∂u/∂ν=huon ∂Ω  ×0,t∗ux,0=u0x≥0in Ω¯. Here Ω⊂℠NN≥3 is a bounded and convex domain with smooth boundary, and constants m,p,q,α are supposed to be positive. Utilizing the Sobolev inequality and the differential inequality technique, lower bound for blow-up time is derived when blow-up occurs. In addition, we give an example as application to illustrate the abstract results obtained in this paper.

Suggested Citation

  • Xuhui Shen & Lun Lan & Julien Bruchon, 2022. "Blow-Up Analysis for a Reaction-Diffusion Model with Nonlocal and Gradient Terms," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-9, March.
    • Handle: RePEc:hin:jnlmpe:4150728
    DOI: 10.1155/2022/4150728
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