Year: 2024
Type: article
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).
Author: Baljinnyam Tsangia
Institution: Mongolian University of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415518849