Well-Posedness Results for a Class of Nonlinear Reaction-Diffusion Equations with Memory

Duy Binh Ho; Duc Phuong Nguyen; Viet Tri Vo

doi:10.61383/ejam.20231125

Authors

Ho Duy Binh Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam
Nguyen Duc Phuong Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Viet Nam Corresponding Author https://orcid.org/0000-0003-3779-197X
Vo Viet Tri Department of Applied Mathematics, Thu Dau Mot University, Binh Duong province, Vietnam

DOI:

https://doi.org/10.61383/ejam.20231125

Keywords:

nonlinear heat equation, reaction-diffusion equations, memory term, blow-up

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.

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