EUDML

This paper concerns the study of the numerical approximation for the following boundary value problem: $\{\begin{matrix} u_{t} (x, t) - u_{x x} (x, t) = - u^{- p} (x, t), & 0 < x < 1, t > 0, u_{x} (0, t) = 0, & u (1, t) = 1, t > 0, u (x, 0) = u_{0} (x) > 0, & 0 \leq x \leq 1, \end{matrix}$ where $p > 0$ . We obtain some conditions under which the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also establish the convergence of the semidiscrete quenching time. Finally, we give some numerical experiments to illustrate our analysis.

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Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions.

Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions.

Blow-up time of some nonlinear wave equations.

Asymptotic behavior for numerical solutions of a semilinear parabolic equation with a nonlinear boundary condition.

Asymptotic behavior for discretizations of a semilinear parabolic equation with a nonlinear boundary condition.

Quenching for semidiscretizations of a semilinear heat equation with Dirichlet and Neumann boundary conditions