Semilinear heat equation with singular terms

Ould Khatri Mohamed Mahmoud and Youssfi Ahmed: Semilinear heat equation with singular terms. (2022)

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The main goal of this paper is to analyze the existence and nonexistence as well as the regularity of positive solutions for the following initial parabolic problem ∂tu − ∆u = µ u |x| 2 f u in ΩT := Ω × (0, T), u = 0 on ∂Ω × (0, T), u(x, 0) = u0(x) in Ω, where Ω ⊂ RN, N ≥ 3, is a bounded open, σ ≥ 0 and µ > 0 are real constants and f ∈ L m(ΩT), m ≥ 1, and u0 are nonnegative functions. The study we lead shows that the existence of solutions depends on σ and the summability of the datum f as well as on the interplay between µ and the best constant in the Hardy inequality. Regularity results of solutions, when they exist, are also provided. Furthermore, we prove uniqueness of finite energy solutions.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 69
ISSN: 1417-3875
Language: English
DOI: 10.14232/ejqtde.2022.1.69
Uncontrolled Keywords: Hőegyenlet - féllineáris
Additional Information: Bibliogr.: p. 30-34. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2023. Mar. 13. 13:19
Last Modified: 2023. Mar. 13. 13:19

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