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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lamya Almaghamsi & Abdeljabbar Ghanmi & Khaled Kefi, 2025. "Existence of Non-Negative Solutions for Parabolic Problem on Riemannian Manifold," Mathematics, MDPI, vol. 13(5), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:801-:d:1601815
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