ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Global Attractor of a Multivalued Dynamical System Generated by a Two-phase Heating System

Author(s):

Dmitry Zyryanov

Saint-Petersburg State University,
Faculty of Mathematics and Mechanics
Chair of Applied Cybernetics
Klychevaya str., 7
195221, St. Petersburg, Russia
Bachelor degree

dmitry.zyr@gmail.com

Volker Reitmann

Saint-Petersburg State University,
Faculty of Mathematics and Mechanics
Chair of Applied Cybernetics
Botanicheskaya ul. 70/2,
198504, Petergof, St. Petersburg, Russia
Professor of the Chair of Applied Cybernetics

vreitmann@aol.com

Abstract:

In this work we study the asymptotic behavior of solutions of Maxwell's equations coupled with the heat equation for the Stefan problem in 3-dimensional space describing a microwave heating process. These results generalize some well-known properties of the one-dimensional heating system. We use in the 3-dimensional case weak solutions which are generated by a couple of integral identities. Based on this solutions a multi-valued dynamical system is constructed and the existence of a global attractor is proved. The resulting multi-valued dynamical system is considered only at a subspace of the solutions space. A numerical experiment for the temperature approximation is carried out.

Keywords

References:

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