| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 254, n. 10, p. 4066-4087, MAY 15 2013. |
| Web of Science Citations: | 24 |
| Abstract | |
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) | |
| FAPESP's process: | 10/12202-9 - Asymptotic stability of nonlinear hyperbolic equations |
| Grantee: | Ma To Fu |
| Support Opportunities: | Regular Research Grants |