| Volume 6, Number 4, 2016, Pages 1041-1048 DOI：10.11948/2016067 |
| Convergence to equilibrium for a time semi-discrete damped wave equation |
| Morgan Pierre,Philippe Rogeon |
| Keywords:{\L}ojasiewicz-Simon inequality, gradient-like equation, backward Euler scheme. |
| Abstract: |
| We prove that the solution of the backward Euler scheme applied to a damped wave equation with analytic nonlinearity converges to a stationary solution as time goes to infinity. The proof is based on the {\L}ojasiewciz-Simon inequality. It is much simpler than in the continuous case, thanks to the dissipativity of the scheme. The framework includes the modified Allen-Cahn equation and the sine-Gordon equation. |
PDF Download reader
|
|
|
|