In this paper, we address the solution of a semilinear heat equation with variable reaction subject to Dirichlet boundary conditions and nonnegative initial datum. Under some assumptions, we show that the solution of the above problem blows up in a finite time, and its blow-up time goes to that of the solution of a certain differential equation. Finally, we give some numerical results to illustrate our analysis.
Semilinear parabolic equation, blow-up, numerical blow-up time
BONI, THEODORE KOUASSI and KOUAKOU, REMI KOUADIO
"Blow-up time for a semilinear parabolic equation with variable reaction,"
Turkish Journal of Mathematics: Vol. 35:
1, Article 7.
Available at: https://journals.tubitak.gov.tr/math/vol35/iss1/7