Long-time behavior of a quasilinear viscoelastic equation with past history

Autor(es)

Araujo, Rawlilson de Oliveira ^[1] ; Ma, To Fu ^[1] ; Qin, Yuming ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Carlos, SP - Brazil

^[2] Donghua Univ, Dept Appl Math, Shanghai 201620 - Peoples R China

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 254, n. 10, p. 4066-4087, MAY 15 2013.
• Citações Web of Science: 24

Resumo

This paper is concerned with a class of quasilinear wave equations with memory vertical bar u(t)vertical bar(rho)u(tt) - alpha Delta u - Delta u(tt) + integral(t)(tau) mu(t - s)Delta u(s)ds - gamma Delta u(t) + f(u) = h, rho > 0, which was considered by several authors, with tau = 0, since 2001. Existing results are mainly devoted to global existence, energy decay, existence with small data and blow-up of,solutions. However uniqueness seems to be an open problem and existence of attractors was no yet considered. The objective of the present paper is to provide some results on the well-posedness and longtime behavior to this equation in a more general setting which includes past history, that is, by taking tau = -infinity in the memory term. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 10/12202-9 - Estabilidade assintótica de equações hiperbólicas não lineares
• Beneficiário: Ma To Fu
• Modalidade de apoio: Auxílio à Pesquisa - Regular