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
- dynamical system
- global attractor
- multi-valued
- Stefan problem
- two-phased system with heating
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