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

Guosheng Zhang and Yifu Wang

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

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.

Date: 2013
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https://doi.org/10.1155/2013/746086

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:746086

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