Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2017, Article ID 4529847, 9 pages
https://doi.org/10.1155/2017/4529847
Research Article

Weak and Strong Solutions for a Strongly Damped Quasilinear Membrane Equation

Department of Mathematics Education, College of Education, Daegu University, Jillyang, Gyeongsan, Gyeongbuk, Republic of Korea

Correspondence should be addressed to Jin-soo Hwang; rk.ca.ugead@gnawhsj

Received 9 February 2017; Accepted 4 April 2017; Published 11 June 2017

Academic Editor: Sining Zheng

Copyright © 2017 Jin-soo Hwang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider a strongly damped quasilinear membrane equation with Dirichlet boundary condition. The goal is to prove the well-posedness of the equation in weak and strong senses. By setting suitable function spaces and making use of the properties of the quasilinear term in the equation, we have proved the fundamental results on existence, uniqueness, and continuous dependence on data including bilinear term of weak and strong solutions.