Quenching phenomena for a non-local diffusion equation with a singular absorption
نویسنده
چکیده
In this paper we study the quenching problem for the non-local diffusion equation ut(x, t) = ∫ Ω J(x− y)u(y, t) dy + ∫ RN\Ω J(x− y) dy − u(x, t)− λu−p(x, t). We prove that there exits a critical parameter λ∗ such that for all λ > λ∗ every solution quenches and for λ ≤ λ∗ there are both global and quenching solutions. For the quenching solutions we study the quenching rate and the quenching set. We also prove that the solutions of properly rescaled non local problems approximate the solution of the semilinear heat equation with u = 1 at the boundary.
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