Almost sure asymptotic stability of fractional stochastic nonlinear heat equation

Almost sure asymptotic stability of fractional stochastic nonlinear heat equation

  • Zineb ARAB Department of Chemistry, Lab. of researches in radiations physics and their interactions with matter (LRPRIM), Faculty of Matter Sciences, University of Hadj Lakhdar Batna, Batna 05008, Algeria
  • Amel REDJIL Department of Mathematics, Faculty of Science, LaPS Laboratory, Badji Mokhtar University, Annaba, Algeria
  • Mahmoud Mohamed El BORAI Department of Mathematics and Computer Sciences, Faculty of Science, Alexandria University, Alexandria 21500, Egypt
DOI: https://doi.org/10.19139/soic-2310-5070-2593
Keywords: Almost sure asymptotic stability, nonlinear heat equation, fractional power of the Laplacian, trace-class noise

Abstract

Recently, the fractional stochastic nonlinear heat equation in the Hilbert space L2(0; 1), driven by the fractional power of the Laplacian and perturbed by a  trace-class noise has been studied by the first and the last authors. They have proved the wellposedness, the pth-moment exponential stability and the almost surely exponential stability of such problem in the semigroup framework. The current work is considered as a continuation of the previousely mentioned paper. More particularly, we establish the almost sure asymptotic stability under the same conditions imposed in our recent work, besides a regularity of the initial condition. Finally, some examples are provided to illustrate the obtained theory.
Published
2025-09-28
How to Cite
ARAB, Z., REDJIL, A., & El BORAI, M. M. (2025). Almost sure asymptotic stability of fractional stochastic nonlinear heat equation. Statistics, Optimization & Information Computing, 14(6), 3310-3320. https://doi.org/10.19139/soic-2310-5070-2593
Issue
Vol 14 No 6 (2025)
Section
Research Articles
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