We investigate the existence of a unique weak solution to a boundary value problem for a non-linear parabolic integro-differential equation. This equation can model heat diffusion phenomena in the case when a nonlinear dependence on a memory term is assumed.The proof of existence relies on a regularization - fixed point - passage to the limit scheme, whereas uniqueness is proved via contractive estimates.
Well posedness for a heat equation with a nonlinear memory term
Schimperna, Giulio
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2023-01-01
Abstract
We investigate the existence of a unique weak solution to a boundary value problem for a non-linear parabolic integro-differential equation. This equation can model heat diffusion phenomena in the case when a nonlinear dependence on a memory term is assumed.The proof of existence relies on a regularization - fixed point - passage to the limit scheme, whereas uniqueness is proved via contractive estimates.File in questo prodotto:
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