Self-similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation

Author(s)

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

Affiliation

^[1] Univ Bari, Dept Math, Via E Orabona 4, I-70124 Bari - Italy

^[2] Univ Sao Paulo, FFCLRP, Dept Comp & Matemat, Av Bandeirantes, 3900 Campus USP, BR-14040901 Ribeirao Preto, SP - Brazil

• Document type: Journal article
• Source: MATHEMATICAL METHODS IN THE APPLIED SCIENCES; v. 40, n. 18, p. 6480-6494, DEC 2017.
• Web of Science Citations: 4

Abstract

In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with critical, structural, dissipation, and absorbing power nonlinearity: u(tt) + Delta(2 theta) u + 2 mu(-)(theta)u(t) + vertical bar u(t)vertical bar(p-1)u(t) = 0, t >= 0, x is an element of R-n, with mu > 0, theta is a positive integer, and p > 1 + 4 theta/n, in space dimension n is an element of (2 theta, 4 theta). We use these estimates to find the self-similar asymptotic profile of the solutions, when mu >= 1. (AU)

• FAPESP's process: 15/16038-2 - Lp-Lq decay estimates for Evolution Operators
• Grantee: Marcelo Rempel Ebert
• Support Opportunities: Regular Research Grants