Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 09, pp. 1-13.

Title: Existence of global weak solutions for a p-Laplacian inequality with strong dissipation in noncylindrical domains
       
Authors: Jorge Ferreira (Federal Fluminense Univ., Volta Redonda, RJ, Brazil)
         Erhan Piskin (Dicle Univ., Diyarbakir, Turkey)
         Mohammad Shahrouzi (Jahrom Univ., Jahrom, Iran)
         Sebastiao Cordeiro (Federal Univ. of Para, Abaetetuba, PA, Brazil)
         Carlos Alberto Raposo (Federal Univ., Sao Joao del-Rei, MG, Brazil)

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

Submitted February 4, 2021. Published January 27, 2022.
Math Subject Classifications: 35Q55, 35B44, 26A33, 35B30.
Key Words: Global solution; weak solutions; p-Laplacian inequality;
           strong dissipation; noncylindrical domain.