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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