Equations of mathematical physics. Radkevich E.V., Palin V.V.

The book contains notes of all lectures held in 2021/2022 and 2022/2023 of the school years on the experimental flow of the Mechanical and Mathematics Faculty of Moscow State University named after MV Lomonosov (Group 341). From a meaningful point of view, the material set forth in the book refers to two different types. Firstly, these are mandatory topics, the inclusion of which in the annual lecture course is generally accepted. These include: classical theory of harmonic functions; Classical theory of Koshi problem for a wave equation; Theory of generalized functions and spaces of Sobolev; Green function and Poisson formula for the Laplace equation; The theory of the task of the Koshi for the thermal conductivity equation; Summarized setting of marginal tasks for the Poisson equation and variations for such tasks.

in order to demonstrate to students modern methods of equations of mathematical physics, the remaining part of the material of the book constitutes additional topics: the principles of a maximum for elliptical equations of a general view; The theory of the existence and uniqueness of the classical solution of the non -fredrychus hyperbolic system of the system of equations in private derivatives of the first order; Monotony method (Minti and Browser method); the introduction into the theory of generalized solutions of the problem of Koshi for the scalar law of conservation; Introduction to the theory of averaging.

The course of lectures is designed for students of universities - mathematicians, physicists and engineers with increased mathematical training.

The book is of interest to students studying the course of mathematical physics, so and for persons specializing in the field of application of equations in private derivatives and their solutions.