Open AccessBoundedness and Finite-Time Stability for Multivalued Doubly-Nonlinear Evolution Systems Generated by a Microwave Heating Problem
Author(s) -
С. А. Попов,
Volker Reitmann,
Sergey Skopinov
Publication year - 2018
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2018-64-1-148-163
Subject(s) - nonlinear system , stability (learning theory) , instability , mathematics , process (computing) , time evolution , microwave , microwave heating , control theory (sociology) , computer science , physics , mechanics , telecommunications , control (management) , quantum mechanics , machine learning , artificial intelligence , operating system
Doubly-nonlinear evolutionary systems are considered. Sucient 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. Sucient conditions for the nite-time stability of a global process and of a local multivalued process are shown. For local multivalued processes sucient conditions for the nite-time instability are derived. For the one-dimensional microwave heating problem conditions of the nite-time stability are shown.