RATE OF ATTRACTION FOR A SEMILINEAR WAVE EQUATION WITH VARIABLE COEFFICIENTS AND CRITICAL NONLINEARITIES

Autor(es)

Araruna, Fagner Dias ^[1] ; Morais Bezerra, Flank David ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Paraiba, Dept Math, BR-58059900 Joao Pessoa, Paraiba - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PACIFIC JOURNAL OF MATHEMATICS; v. 266, n. 2, p. 257-282, DEC 2013.
• Citações Web of Science: 3

Resumo

We study the rate of convergence of global attractors and eigenvalues of the family of dissipative semilinear wave equations with variable coefficients u(tt) + Lambda(epsilon)u + Lambda(delta)(epsilon)u(t) = f(u), where Lambda(epsilon) is the elliptic operator -div(a(epsilon)(x)del) with epsilon is an element of {[}0, 1] and sufficiently smooth coefficients a(epsilon), and where delta is an element of (1/2, 1) and the nonlinearity f is a continuously differentiable function satisfying suitable growth conditions. We show that the rate of convergence, as epsilon -> 0(+), of the global attractors of these problems, as well as of their eigenvalues, is proportional to the distance of the coefficients parallel to a(epsilon) - a(0)parallel to(L infinity(Omega)). (AU)

• Processo FAPESP: 11/04166-5 - Continuidade de atratores para problemas parabólicos
• Beneficiário: Marcelo José Dias Nascimento
• Modalidade de apoio: Auxílio à Pesquisa - Regular