A class of parabolic fractional reaction-diffusion systems with control of total mass: Theory and numerics - Maha Daoud (ENSTA)

In this talk based on, we present some new results about global-in-time existence of strong solutions to a class of parabolic fractional reaction–diffusion systems posed in a bounded open subset of R^d. The nonlinear reactive terms are assumed to satisfy natural structure conditions which provide nonnegativity of the solutions and uniform control of the total mass. The diffusion operators are of type u_i → d_i(−∆)^(s_i) u_i where 0 < s_i < 1. For more details about this kind of operators, we refer the interested reader to [3] and references therein. Global existence of strong solutions is proved under the assumption that the reactive terms are at most of polynomial growth. Our results extend previous results obtained in [4, 5] where the diffusion operators are of type u_i → −d_i∆u_i.

Also, we present some numerical simulations in order to examine the global existence of solutions to systems with exponentially growing right-hand sides, which remains so far an open theoretical question even in the case where the diffusion is driven by the classical Laplacian.