Boundedness and Finite-Time Stability for Multivalued Doubly-Nonlinear Evolution Systems Generated by a Microwave Heating Problem

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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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