Well-posedness of the microwave heating problem
Journal: Discrete and Continuous Models and Applied Computational Science (Vol.32, No. 2)Publication Date: 2024-11-02
Authors : Baljinnyam Tsangia;
Page : 222-233
Keywords : evolutionary problems; nonlinear perturbation; Lipschitz continuous; quadratic form; coupled problems;
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).
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Last modified: 2024-11-02 04:40:31