Author:
Ferreira Jorge,Piskin Erhan,Shahrouzi Mohammad,Cordeiro Sebastiao
Abstract
In this work, we obtain global solutions for nonlinear inequalities of p-Laplacian type in noncylindrical domains, for the unilateral problem with strong dissipation $$ u'' -\Delta _pu-\Delta u'-f\geq 0\quad\text{in }Q_0,$$ where \(\Delta _p\) is the nonlinear p-Laplacian operator with \(2\leq p<\infty\), and \(Q_0\) is the noncylindrical domain. Our proof is based on a penalty argument by J. L. Lions and Faedo-Galerkin approximations
Reference22 articles.
1. A. Aibeche, S. Hadi, A. Sengouga; Asymptotic behaviour of nonlinear wave equations in a noncylindrical domain becoming unbounded, Electr. J. differ. Equ., 2017 (2017), no. 288, 1-15.
2. N. G. Andrade; On one-sided problem connected with a nonlinear system of partial differential equation , An. Acad. Bras. Ciencias, 54 (1982), 613-618.
3. P. Ballard, S. Basseville; Existence and uniqueness for dynamical unilateral contact with Coulomb friction: a model problem, ESAIM - Math. Model. Num., 39 (2005), 59-77.
4. I. Chueshov, I. Lasiecka; Existence, uniqueness of weak solution and global attactors for a class of nonlinear 2D Kirchho -Boussinesq models, Discrete Contin. Dyn. Syst., 15 (2006), 777-809.
5. M. Dreher; The wave equation for the p-Laplacian, Hokkaido Math. J., 36 (2007), 21-52.