Well posedness for a heat equation with a nonlinear memory term: Well posedness for a heat equation: G. Schimperna, A. S. Rafeeq.

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. [ABSTRACT FROM AUTHOR]