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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Asymptotic profiles and critical exponents for a semilinear damped plate equation with time-dependent coefficients

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D'Abbicco, Marcello [1] ; Ebert, Marcelo Rempel [2]
Total Authors: 2
[1] Univ Bari, Dept Math, Via E Orabona 4, I-70125 Bari - Italy
[2] Univ Sao Paulo, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: ASYMPTOTIC ANALYSIS; v. 123, n. 1-2, p. 1-40, 2021.
Web of Science Citations: 0

In this paper we study the asymptotic profile (as t -> infinity) of the solution to the Cauchy problem for the linear plate equation u(tt) + Delta(2)u - lambda(t)Delta u + u(t) = 0 when lambda = lambda(t) is a decreasing function, assuming initial data in the energy space and verifying a moment condition. For sufficiently small data, we find the critical exponent for global solutions to the corresponding problem with power nonlinearity u(tt) + Delta(2)u - lambda(t)Delta u + u(t) = vertical bar u vertical bar(p). In order to do that, we assume small data in the energy space and, possibly, in L-1. In this latter case, we also determinate the asymptotic profile of the solution to the semilinear problem for supercritical power nonlinearities. (AU)

FAPESP's process: 17/19497-3 - Asymptotic profile of solutions for some evolution partial differential equations and applications
Grantee:Marcelo Rempel Ebert
Support Opportunities: Regular Research Grants