CPAA
On the Lyapunov functions for the solutions of the generalized Burgers equation
Ezzeddine Zahrouni
Communications on Pure & Applied Analysis 2003, 2(3): 391-410 doi: 10.3934/cpaa.2003.2.391
We derive new Lyapunov functions not arising from energy norm for global solutions of Generalized Burgers Equation with initial data in homogeneous Besov spaces.
keywords: smoothness Besov spaces Lyapunov functions. global existence generalized Burgers equation
CPAA
On a time discretization of a weakly damped forced nonlinear Schrödinger equation
Olivier Goubet Ezzeddine Zahrouni
Communications on Pure & Applied Analysis 2008, 7(6): 1429-1442 doi: 10.3934/cpaa.2008.7.1429
We consider a semi-discrete in time Crank-Nicolson scheme to discretize a damped forced nonlinear Schrödinger equation. This provides us with a discrete infinite-dimensional dynamical system. We prove the existence of a finite dimensional global attractor for this dynamical system.
keywords: nonlinear Schrödinger equations. Global Attractor Crank-Nicolson scheme
CPAA
Regularity of the attractor for a coupled Klein-Gordon-Schrödinger system with cubic nonlinearities in $\mathbb{R}^2$
Salah Missaoui Ezzeddine Zahrouni
Communications on Pure & Applied Analysis 2015, 14(2): 695-716 doi: 10.3934/cpaa.2015.14.695
we prove the existence of a global attractor to dissipative Klein-Gordon-Schrödinger (KGS) system with cubic nonlinearities in $H^1({\mathbb R}^2)\times H^1({\mathbb R}^2)\times L^2({\mathbb R}^2)$ and more particularly that this attractor is in fact a compact set of $H^2({\mathbb R}^2)\times H^2({\mathbb R}^2)\times H^1({\mathbb R}^2)$.
keywords: Klein-Gordon-Schrödinger equation global attractor asymptotic compactness.
CPAA
Stability and convergence of an hybrid finite volume-finite element method for a multiphasic incompressible fluid model
Caterina Calgaro Meriem Ezzoug Ezzeddine Zahrouni
Communications on Pure & Applied Analysis 2018, 17(2): 429-448 doi: 10.3934/cpaa.2018024

In this paper, we construct a fully discrete numerical scheme for approximating a two-dimensional multiphasic incompressible fluid model, also called the Kazhikhov-Smagulov model. We use a first-order time discretization and a splitting in time to allow us the construction of an hybrid scheme which combines a Finite Volume and a Finite Element method. Consequently, at each time step, one only needs to solve two decoupled problems, the first one for the density and the second one for the velocity and pressure. We will prove the stability of the scheme and the convergence towards the global in time weak solution of the model.

keywords: Kazhikhov-Smagulov model finite volume method finite element method stability convergence

Year of publication

Related Authors

Related Keywords

[Back to Top]