This paper deals with the study of a nonlinear parabolic equation with nonlinear memory subject to Dirichlet boundary conditions and positive initial datum. Under some assumptions, we show that the solution of the above problem blows up in the finite time and estimate its blow-up time. We also prove the continuity of the blow-up time as a function of the initial datum. Finally, we give some numerical results to illustrate our analysis.

nonlinear parabolic equation, numerical blow-up time, nonlinear memory, continuity, Dirichlet boundary conditions.

Received: April 17, 2021; Accepted: May 25, 2021; Published: June 3, 2021

How to cite this article:  N’gohisse Konan Firmin, Camara Zié and Yoro Gozo, Continuity of the Blow-Up Time in a Nonlinear Parabolic Equation With Nonlinear Memory, International Journal of Numerical Methods and Applications 20(1) (2021), 55-75. DOI 10.17654/NM020010055

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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