Quenching phenomena for a non-local diffusion equation with a singular absorption

In this paper we study the quenching problem for the non-local diffusion equation

ut(x,t) = òW J(x - y)u(y,t)dy + ò\mathbbRN\W J(x - y)dy - u(x,t) - lu - p(x,t) {u_t}(x,t) = \int\limits_\Omega {J(x - y)u(y,t)dy + \int\limits_{{\mathbb{R}^N}\backslash \Omega } {J(x - y)dy - u(x,t) - \lambda {u^{ - p}}(x,t)} }
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