An application of L-p - L-q decay estimates to the semi-linear wave equation with parabolic-like structural damping

Author(s)

D'Abbicco, M. ^[1] ; Ebert, M. R. ^[2]

Affiliation

^[1] Univ Bari, Dipartimento Matemat, I-70125 Bari - Italy

^[2] Univ Sao Paulo, FFCLRP, Dept Comp & Matemat, BR-14040901 Ribeirao Preto - Brazil

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS; v. 99, p. 16-34, APR 2014.
• Web of Science Citations: 17

Abstract

In this paper we study the global existence of small data solutions to u(tt) - Delta u + 2a(-Delta)(sigma) u(t) = |u|(p), u(0, x) = u(0)(x), u(t)(0, x) = u(1)(x), where a > 0, sigma is an element of (0, 1/2] and p > 1. Assuming small data in some Sobolev spaces, we obtain the global existence for p > 1 + 2/(n - 2 sigma), in space dimension n <= (n) over bar, where (n) over bar = (n) over bar(sigma) NE arrow infinity as sigma -> 1/2. In particular, our result holds in any space dimension n >= 2 if sigma = 1/2. (C) 2014 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 12/19085-3 - Global existence for a class of semi-linear wave equations with variable coefficients
• Grantee: Marcelo Rempel Ebert
• Support Opportunities: Research Grants - Visiting Researcher Grant - International