CONVERGENCE TO EQUILIBRIUM FOR A TIME SEMI-DISCRETE DAMPED WAVE EQUATION

Morgan Pierre; Philippe Rogeon

doi:10.11948/2016067

2016 Volume 6 Issue 4

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Morgan Pierre, Philippe Rogeon. CONVERGENCE TO EQUILIBRIUM FOR A TIME SEMI-DISCRETE DAMPED WAVE EQUATION[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1041-1048. doi: 10.11948/2016067

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Morgan Pierre, Philippe Rogeon. CONVERGENCE TO EQUILIBRIUM FOR A TIME SEMI-DISCRETE DAMPED WAVE EQUATION[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1041-1048. doi: 10.11948/2016067

CONVERGENCE TO EQUILIBRIUM FOR A TIME SEMI-DISCRETE DAMPED WAVE EQUATION

Laboratoire de Mathématiques et Applications UMR CNRS 7348, Université de Poitiers, Téléport 2-BP 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France

Abstract

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 Łojasiewciz-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.
- Ł /
- ojasiewicz-Simon inequality /
- gradient-like equation
MSC: 65M12;65P05

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References

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