Arij Bouzelmate, Fatima Sennouni, Abdelilah Gmira, "The Quenching Solutions of a Singular Parabolic Equation," WSEAS Transactions on Mathematics, vol. 22, pp. 888-893, 2023, DOI:10.37394/23206.2023.22.97
Arij Bouzelmate, Fatima Sennouni, Abdelilah Gmira. The Quenching Solutions of a Singular Parabolic Equation.
WSEAS Transactions on Mathematics. 2023;22:888-893. 10.37394/23206.2023.22.97
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.
Keywords:
Singular parabolic equation, Self-similar solutions, Quenching solutions, Existence of solutions, Asymptotic behavior
Pages: 888-893 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 22, 2023, Art. #97 DOI: 10.37394/23206.2023.22.97
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