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Contemporary Mathematics. Fundamental Directions, 2018, Volume 64, Issue 1, Pages 148–163
DOI: https://doi.org/10.22363/2413-3639-2018-64-1-148-163 (Mi cmfd351) 		 
Boundedness and finite-time stability for multivalued doubly-nonlinear evolution systems generated by a microwave heating problem

S. Popov, V. Reitmann, S. Skopinov

St. Petersburg State University, St. Petersburg, Russia
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DOI: https://doi.org/10.22363/2413-3639-2018-64-1-148-163
Abstract: Doubly-nonlinear evolutionary systems are considered. Sufficient conditions of the boundedness of solutions of such systems are derived. Analogical results for a one-dimensional microwave heating problem are proved. The notions of global process and of a local multivalued process are introduced. Sufficient conditions for the finite-time stability of a global process and of a local multivalued process are shown. For local multivalued processes sufficient conditions for the finite-time instability are derived. For the one-dimensional microwave heating problem conditions of the finite-time stability are shown.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-2858.2018.1
German Academic Exchange Service (DAAD)
Document Type: Article
UDC: 517.957
Language: Russian
Citation: S. Popov, V. Reitmann, S. Skopinov, “Boundedness and finite-time stability for multivalued doubly-nonlinear evolution systems generated by a microwave heating problem”, Differential and functional differential equations, CMFD, 64, no. 1, Peoples' Friendship University of Russia, M., 2018, 148–163
Citation in format AMSBIB
\Bibitem{PopReiSko18}
\by S.~Popov, V.~Reitmann, S.~Skopinov
\paper Boundedness and finite-time stability for multivalued doubly-nonlinear evolution systems generated by a~microwave heating problem
\inbook Differential and functional differential equations
\serial CMFD
\yr 2018
\vol 64
\issue 1
\pages 148--163
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd351}
\crossref{https://doi.org/10.22363/2413-3639-2018-64-1-148-163}
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