Existence of Non-Negative Solutions for Parabolic Problem on Riemannian Manifold

Lamya Almaghamsi, Abdeljabbar Ghanmi and Khaled Kefi ()
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Lamya Almaghamsi: Department of Mathematics and Statistics, College of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Abdeljabbar Ghanmi: Department of Mathematics and Statistics, College of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia
Khaled Kefi: Center for Scientific Research and Entrepreneurship, Northern Border University, Arar 73213, Saudi Arabia

Mathematics, 2025, vol. 13, issue 5, 1-9

Abstract: In this paper, we investigate a perturbed parabolic problem involving the Laplace–Beltrami operator on a smooth compact Riemannian manifold M . For a strongly local Dirichlet form in L 2 ( M ) . More precisely, we begin by proving that, in the case of the existence of a non-negative solution, the potential can be written as a derivative of some functions which are locally integrable on M ; after that, we prove the existence of a non-negative solution for such problems.

Keywords: heat equation; Dirichlet form; Riemannian manifold (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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