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Stability of uniform attractors of impulsive multi-valued semiflows
Affiliation:1. Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wrocław, Poland;2. Department of Mathematics and Statistics, University of Helsinki, Helsinki FI-00014, Finland;3. Departamento de Matemáticas, Universidad de Oviedo, Oviedo, Spain;1. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine;2. Institute for Applied System Analysis, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine;3. Institute of Applied Mathematics and Mechanics of the NASU, Sloviansk, Ukraine;1. Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Trindade, Florianópolis - SC, Brazil;2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos - SP, Brazil;3. Departamento de Matemática e Estatística, Universidade Estadual de Ponta Grossa, Ponta Grossa - PR, Brazil;1. Universidade Estadual Paulista (UNESP), Instituto de Geociências e Ciências Exatas, Câmpus de Rio Claro, Avenida 24-A, 1515, Bela Vista, Rio Claro, São Paulo 13506-900, Brazil;2. Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil
Abstract:In this paper we investigate stability of uniformly attracting sets for semiflows generated by impulsive infinite-dimensional dynamical systems without uniqueness. Obtained abstract results are applied to weakly nonlinear parabolic system, whose trajectories have jumps at moments of intersection with certain surface in the phase space.
Keywords:Attractors  Impulsive systems  Stability  Infinite dimensional multivalued semiflows  Nonlinear parabolic systems
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