Quenching for a nonlinear diffusion equation with a singular boundary condition

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Abstract.

We study a nonlinear diffusion equation \((\psi (u))_t =u_{xx},\0 < x < 1,\t > 0\) with a singular boundary condition \(u_x(1,t) = -g(u(1,t))\) . We prove finite time quenching for the solution. We also establish results on quenching set and rate.

Received: January 28, 1998