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Well-posedness of the microwave heating problem

Journal: Discrete and Continuous Models and Applied Computational Science (Vol.32, No. 2)

Publication Date:

Authors : ;

Page : 222-233

Keywords : evolutionary problems; nonlinear perturbation; Lipschitz continuous; quadratic form; coupled problems;

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Abstract

A number of initial boundary-value problems of classical mathematical physics is generally represented in the linear operator equation and its well-posedness and causality in a Hilbert space setting was established. If a problem has a unique solution and the solution continuously depends on given data, then the problem is called well-posed. The independence of the future behavior of a solution until a certain time indicates the causality of the solution. In this article, we established the well-posedness and causality of the solution of the evolutionary problems with a perturbation, which is defined by a quadratic form. As an example, we considered the coupled system of the heat and Maxwell’s equations (the microwave heating problem).

Last modified: 2024-11-02 04:40:31