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Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source

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  • Guosheng Zhang
  • Yifu Wang

Abstract

This paper is concerned with a nonlocal nonlinear diffusion equation with Dirichlet boundary condition and a source ut(x,t)=∫-∞+∞ J((x-y)/u(y,t) )dy-u(x,t)+up(x,t), x ∈ (−L, L), t > 0, u(x, t) = 0, x ∉ (−L, L), t ≥ 0, and u(x, 0) = u0(x) ≥ 0, x ∈ (−L, L), which is analogous to the local porous medium equation. First, we prove the existence and uniqueness of the solution as well as the validity of a comparison principle. Next, we discuss the blowup phenomena of the solution to this problem. Finally, we discuss the blowup rates and sets of the solution.

Suggested Citation

  • Guosheng Zhang & Yifu Wang, 2013. "Blowup for Nonlocal Nonlinear Diffusion Equations with Dirichlet Condition and a Source," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:746086
    DOI: 10.1155/2013/746086
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    References listed on IDEAS

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    1. Paul Fife, 2003. "Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions," Springer Books, in: Markus Kirkilionis & Susanne Krömker & Rolf Rannacher & Friedrich Tomi (ed.), Trends in Nonlinear Analysis, chapter 3, pages 153-191, Springer.
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