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EnglishIn this Ph.D. thesis, we study a semilinear wave equation with nonlinear and time-dependent damping term. After rewriting the equation as a first order system, we define a class of approximate solutions employing typical tools of hyperbolic systems of conservation laws, such as the Riemann problem. We prove that the initial-boundary value problem is well-posed for initial data in $L^\infty$ space. By recasting the problem as a discrete-time nonhomogeneous system, which is related to a probabilistic interpretation of the solution, we provide a strategy to study its long-time behavior uniformly with respect to the mesh size parameter $\DX=1/N\to 0$. The proof makes use of the Birkhoff decomposition of doubly stochastic matrices and of accurate estimates on the iteration system as $N\to\infty$. Under appropriate assumptions on the nonlinearity, we prove the exponential convergence in $L^\infty$ of the solution to the first order system towards a stationary solution, as $t\to+\infty$, as well as uniform error estimates for the approximate solutions.
Decay in W^{1,\infty} for the 1D semilinear damped wave equation on a bounded domain / Aqel, Fatima Al-Zahra' A N. - (2020 Sep 04).
| Titolo: | Decay in W^{1,\infty} for the 1D semilinear damped wave equation on a bounded domain |
| Autori: | |
| Data di pubblicazione: | 4-set-2020 |
| Citazione: | Decay in W^{1,\infty} for the 1D semilinear damped wave equation on a bounded domain / Aqel, Fatima Al-Zahra' A N. - (2020 Sep 04). |
| Handle: | http://hdl.handle.net/11697/156611 |
| Appare nelle tipologie: | 8.1 Tesi di dottorato |
File in questo prodotto:
| File | Descrizione | Tipologia | Licenza | |
|---|---|---|---|---|
| PhD Thesis - Fatima Alzahra A.pdf | Decay in $W^{1,\infty}$ for the 1D semilinear damped wave equation on a bounded | Tesi di dottorato | Open Access Visualizza/Apri |
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