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Well-posedness of a reaction–diffusion model with stochastic dynamical boundary conditions

Author

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  • Maurelli, Mario
  • Morale, Daniela
  • Ugolini, Stefania

Abstract

We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical reaction of sulphur dioxide with calcium carbonate stones. The boundary condition is given by a Jacobi process, solution to a stochastic differential equation with a mean-reverting drift and a bounded diffusion coefficient. The main result is the global existence and the pathwise uniqueness of mild solutions. The proof relies on a splitting strategy, which allows to deal with the low regularity of the dynamical boundary condition.

Suggested Citation

  • Maurelli, Mario & Morale, Daniela & Ugolini, Stefania, 2025. "Well-posedness of a reaction–diffusion model with stochastic dynamical boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:spapps:v:186:y:2025:i:c:s0304414925000870
    DOI: 10.1016/j.spa.2025.104646
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