LOCAL WELL POSEDNESS, ASYMPTOTIC BEHAVIOR AND ASYMPTOTIC BOOTSTRAPPING FOR A CLASS OF SEMILINEAR EVOLUTION EQUATIONS OF THE SECOND ORDER IN TIME

Autor(es)

Carvalho, A. N. ^[1] ; Cholewa, J. W. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, BR-13560970 Sao Carlos, SP - Brazil

^[2] Silesian Univ, Inst Math, PL-40007 Katowice - Poland

• Tipo de documento: Artigo Científico
• Fonte: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY; v. 361, n. 5, p. 2567-2586, 2009.
• Citações Web of Science: 10

Resumo

A class of semilinear evolution equations of the second order in time of the form u(tt)+Au+mu Au(t)+Au(tt) = f(u) is considered, where -A is the Dirichlet Laplacian, 92 is a smooth bounded domain in R(N) and f is an element of C(1) (R, R). A local well posedness result is proved in the Banach spaces W(0)(1,p)(Omega)xW(0)(1,P)(Omega) when f satisfies appropriate critical growth conditions. In the Hilbert setting, if f satisfies all additional dissipativeness condition, the nonlinear Semigroup of global solutions is shown to possess a gradient-like attractor. Existence and regularity of the global attractor are also investigated following the unified semigroup approach, bootstrapping and the interpolation-extrapolation techniques. (AU)

• Processo FAPESP: 03/10042-0 - Sistemas dinâmicos não lineares e aplicações
• Beneficiário: Alexandre Nolasco de Carvalho
• Linha de fomento: Auxílio à Pesquisa - Programa PRONEX - Temático