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Preprints, Working Papers, ... Year : 2023

On some nonlocal parabolic reaction-diffusion systems with gradient source terms

Abstract

The present paper is concerned with a class of nonlocal parabolic reaction-diffusion systems set in a regular bounded open subset of R N , where the gradients of the unknowns act as source terms . First, we establish some nonexistence and blow-up in finite time results. Second, we prove some new weighted regularity results. Such results are interesting in themselves and play a crucial role to study local existence of nonnegative solutions to our systems under suitable assumptions on the data. This work also highlights a substantial difference between the nonlocal case and the local case already studied by the fourth author and his coworkers.
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Dates and versions

hal-03954680 , version 1 (24-01-2023)

Identifiers

  • HAL Id : hal-03954680 , version 1

Cite

Somia Atmani, Kheireddine Biroud, Maha Daoud, El-Haj Laamri. On some nonlocal parabolic reaction-diffusion systems with gradient source terms. 2023. ⟨hal-03954680⟩
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