Existence and Uniqueness of Blow-up Solutions for a Parabolic Problem with a Localized Nonlinear Term via Semi-group Theory
Résumé
Here, we use the semigroup theory to establish the existence, uniqueness and blow-up for a classical solution of a semilinear parabolic problem with localized nonlinear term| a locally Lipschitz continuous function of the value of the solution at a point of a 1-dimensional domain. Our method, which uses Sobolev spaces and fractional power of operators, is in contrast with the classical ones (Green functions) which supply similar results in 1-dimensional settings.
Domaines
Matériaux et structures en mécanique [physics.class-ph] Matériaux et structures en mécanique [physics.class-ph] Mécanique des matériaux [physics.class-ph] Mécanique des matériaux [physics.class-ph] Mécanique des solides [physics.class-ph] Mécanique des solides [physics.class-ph] Mécanique des structures [physics.class-ph] Mécanique des structures [physics.class-ph]Origine | Fichiers produits par l'(les) auteur(s) |
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