Well-posedness results for a class of nonlinear reaction-diffusion equations with memory

Abstract

In this paper, we are interested to study the initial value problem for nonlinear heat equation with memory.  For our problem, we show that the local existence theory related to the finite time blow-up is also obtained for the problem with logarithmic nonlinearity. We also obtain the blowup continuation property of the mild solution. The principal techniques based on some Sobolev embeddings with \(L^p\) spaces.