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math.NA2024
A numerical study of a PDE-ODE system with a stochastic dynamical boundary condition: a nonlinear model for sulphation phenomena
Francesca Arceci, Daniela Morale, Stefania Ugolini
We investigate the qualitative behaviour of the solutions of a stochastic boundary value problem on the half-line for a nonlinear system of parabolic reaction-diffusion equations,…
math.PR2024
A Feynman--Kac representation of a non-conservative and path-dependent nonlinear reaction-diffusion-advection system
Daniela Morale, Leonardo Tarquini, Stefania Ugolini
We provide a probabilistic interpretation of a weakly parabolic PDE--ODE system with a reaction term, which makes the dynamics non-conservative. As a consequence, the solution is r…