WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 22, 2023
The Quenching Solutions of a Singular Parabolic Equation
Authors: , ,
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: $$(E): ut(x,t)=(u^{m})_{xx}(x,t)-|x|^{q}u^{-p}(x,t), \in \mathbb{R}, t>0$$ 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.