Well-posedness results for a class of nonlinear reaction-diffusion equations with memory
Authors
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Ho Duy Binh
Division of Applied Mathematics, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam
https://orcid.org/0000-0002-8827-5812
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Nguyen Duc Phuong
Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Viet Nam
https://orcid.org/0000-0003-3779-197X
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Vo Viet Tri
Department of Applied Mathematics, Thu Dau Mot University, Binh Duong province, Vietnam
https://orcid.org/0000-0002-9775-8007
https://doi.org/10.61383/ejam.20231125
Keywords:
nonlinear heat equation, reaction-diffusion equations, memory term, blow-upAbstract
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.References
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Copyright (c) 2023 Electronic Journal of Applied Mathematics
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2023 May 04
Published 2023 May 07
