QUENCHING FOR A REACTION-DIFFUSION EQUATION WITH WEAK SINGULARITIES

QUENCHING FOR A REACTION-DIFFUSION EQUATION WITH WEAK SINGULARITIES

B. Selcuk

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Abstract

This paper studies the following reaction-di usion equation with a weak singular boundary condition. The primary objective for this problem is to analyze the quenching properties. It is obtained that  nite time quenching occurs on the left bound- ary, the time derivative of the solution blows up at the same time and also quench- ing rate estimates of the solution of the eqaution kt(x; t) = kxx(x; t) + ln  k(x; t), (x; t) 2 (0; 1)   (0; T) with kx (0; t) = ????ln  k(0; t), kx (1; t) = 0, t 2 (0; T) and ini- tial function k (x; 0) = k0 (x) with [0; 1] ! (0; 1) where 0 <  ;   < 1 and T is a  nite time.

Keywords

Reaction-di usion equation, Singular boundary condition, Quenching, Max- imum principles.