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Journals and Conferences
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.
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.
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.