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Well posedness for a heat equation with a nonlinear memory term

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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.

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Correspondence to Giulio Schimperna.

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Communicated by G. D. Veerappa Gowda.

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Schimperna, G., Rafeeq, A.S. Well posedness for a heat equation with a nonlinear memory term. Indian J Pure Appl Math (2023).

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