Boundedness and Finite-Time Stability for Multivalued Doubly-Nonlinear Evolution Systems Generated by a Microwave Heating Problem
- Authors: Popov S1, Reitmann V1, Skopinov S1
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Affiliations:
- St. Petersburg State University
- Issue: Vol 64, No 1 (2018): Differential and Functional Differential Equations
- Pages: 148-163
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/22266
- DOI: https://doi.org/10.22363/2413-3639-2018-64-1-148-163
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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.
About the authors
S Popov
St. Petersburg State University
Email: psa.87@mail.ru
St. Petersburg, Russia
V Reitmann
St. Petersburg State University
Email: vreitmann@aol.com
St. Petersburg, Russia
S Skopinov
St. Petersburg State University
Email: serg_vologda@mail.ru
St. Petersburg, Russia
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