The Quenching Solutions of a Singular Parabolic Equation

Abstract

This article is dedicated to the study of the self-similar solutions of a nonlinear parabolic equation. More precisely, we consider the following uni-dimensional equation: (E) : ut(x, t) = (u m)_xx(x, t) − |x|^q u^−p (x, t), x ∈ R, t > 0, where m > 1, q > 1 and p > 0. Initially, we employed a fixed point theorem and an associated energy function to establish the existence of solutions. Subsequently, we derived some important results on the asymptotic behavior of solutions near the origin.