Table of Contents
ISRN Mathematical Analysis
Volume 2013, Article ID 268505, 13 pages
http://dx.doi.org/10.1155/2013/268505
Research Article

On Global Existence of Solutions of the Neumann Problem for Spherically Symmetric Nonlinear Viscoelasticity in a Ball

1Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, Kaliskiego 2, 00-908 Warsaw, Poland
2Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland

Received 21 November 2012; Accepted 20 December 2012

Academic Editors: G. Akrivis, L. Wang, and C. Zhu

Copyright © 2013 Jerzy A. Gawinecki and Wojciech M. Zajączkowski. 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 examine spherically symmetric solutions to the viscoelasticity system in a ball with the Neumann boundary conditions. Imposing some growth restrictions on the nonlinear part of the stress tensor, we prove the existence of global regular solutions for large data in the weighted Sobolev spaces, where the weight is a power function of the distance to the centre of the ball. First, we prove a global a priori estimate. Then existence is proved by the method of successive approximations and appropriate time extension.