Attractors for the strongly damped wave equation with p-Laplacian

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Khanmamedov A., ŞEN Z.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.40, no.12, pp.4436-4447, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 12
  • Publication Date: 2017
  • Doi Number: 10.1002/mma.4315
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4436-4447
  • Hacettepe University Affiliated: Yes

Abstract

This paper is concerned with the initial-boundary value problem for one-dimensional strongly damped wave equation involving p-Laplacian. For p > 2, we establish the existence of weak local attractors for this problem in W-0(1,p)(0,1) x L-2(0, 1) Under restriction 2 < p < 4, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in W-0(1,p)(0,1) x L-2(0, 1), and this attractor is a bounded subset of W-1,W-infinity(0,1) x W-1,W-infinity(0,1). Copyright (C) 2017 JohnWiley & Sons, Ltd.