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Pré-Publication, Document De Travail Année : 2023

A class of fractional parabolic reaction-diffusion systems with control of total mass

Maha Daoud
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  • PersonId : 1260962
El-Haj Laamri
Azeddine Baalal
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  • PersonId : 1045685

Résumé

In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems posed in a bounded domain of $R ^N$. The nonlinear reactive terms are assumed to satisfy natural structure conditions which provide non-negativity of the solutions and uniform control of the total mass. The diffusion operators are of type $u_i → d_i (−∆) ^s u _i$ where $0 < s < 1$. Global existence of strong solutions is proved under the assumption that the nonlinearities are at most of polynomial growth. Our results extend previous results obtained when the diffusion operators are of type $u_i → −d _i ∆u_ i$. On the other hand, we use numerical simulations 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 s = 1.
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Dates et versions

hal-04123268 , version 1 (09-06-2023)

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Maha Daoud, El-Haj Laamri, Azeddine Baalal. A class of fractional parabolic reaction-diffusion systems with control of total mass: theory and numerics. 2023. ⟨hal-04123268⟩
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