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

Autor(es)

D'Abbicco, Marcello ^[1] ; Ebert, Marcelo Rempel ^[2]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: ASYMPTOTIC ANALYSIS; v. 123, n. 1-2, p. 1-40, 2021.
• Citações Web of Science: 0

Resumo

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)

• Processo FAPESP: 17/19497-3 - Comportamento assintótico de soluções para uma classe de equações diferenciais parciais de difusão e aplicações
• Beneficiário: Marcelo Rempel Ebert
• Modalidade de apoio: Auxílio à Pesquisa - Regular