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


Dmitry Zyryanov

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

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


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.



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