## 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.