Abstract
We study trajectory attractors of autonomous dissipative hyperbolic equations depending on a small parameter ε ≥ 0. We assume that the interaction function of perturbed equation (with ε > 0) can be of arbitrary polynomial growth so that the corresponding Cauchy problem can have a nonunique solution. We prove that the trajectory attractors A ε are upper semicontinuous as ε → 0+ in an appropriate topological space. Two different perturbation problems are considered.
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Chepyzhov, V.V., Vishik, M.I. (1999). Perturbation of trajectory attractors for dissipative hyperbolic equations. In: Rossmann, J., Takáč, P., Wildenhain, G. (eds) The Maz’ya Anniversary Collection. Operator Theory: Advances and Applications, vol 110. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8672-7_4
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DOI: https://doi.org/10.1007/978-3-0348-8672-7_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9725-9
Online ISBN: 978-3-0348-8672-7
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