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For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of solutions is investigated.

- Mohammed Aassila
- Appl. Math. Lett.
- 2001

- Mohammed Aassila
- 2010

In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.

We prove the existence and uniqueness of a global solution of a damped quasilinear hyperbolic equation. Key point to our proof is the use of the Yosida approximation. Furthermore, we apply a method based on a specific integral inequality to prove that the solution decays exponentially to zero when the time t goes to infinity.

- Mohammed Aassila
- Applied Mathematics and Computation
- 2003

We study a unilateral problem for the nonhomogeneous degenerated Kirchhoff equation with a blowing up term. Making use of the penalty method and Galerkin s approximations, we establish global existence and uniqueness theorems. 2002 Published by Elsevier Science Inc.

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