Global existence and blow-up of solution for some fractional reaction- diffusion problems
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Date
2024
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University of Oum El Bouaghi
Résumé
This memory is concerned with studying the problem of existence and non-existence for the global solutions of a diffusion-reaction type equation with fractional derivatives according to Caputo's approach.
The proofs rely on the fixed point principle to prove the existence of a local solution, then on Kaplan's method to determine sufficient conditions to prove the globel existence, as well as sufficient conditions to prove the non-existence (blow-up ) of solutions.
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Mots-clés
Caputo fractional derivative; Reaction-diffusion equation; Global solution