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Systems with local and nonlocal diffusions, mixed boundary conditions, and reaction terms. (English) Zbl 1470.35381

Summary: We study systems with different diffusions (local and nonlocal), mixed boundary conditions, and reaction terms. We prove existence and uniqueness of the solutions and then analyze global existence vs blow up in finite time. For blowing up solutions, we find asymptotic bounds for the blow-up rate.

MSC:

35R09 Integro-partial differential equations
35B40 Asymptotic behavior of solutions to PDEs
35K57 Reaction-diffusion equations
35B44 Blow-up in context of PDEs
35K51 Initial-boundary value problems for second-order parabolic systems
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