Well posedness for a heat equation with a nonlinear memory term

Giulio Schimperna () and Ava Shafeeq Rafeeq ()
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Giulio Schimperna: Università di Pavia
Ava Shafeeq Rafeeq: University of Zakho

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 273-284

Abstract: 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.

Keywords: Existence and uniqueness; Weak solution; Semilinear partial differential equation; Memory kernel (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00478-z

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