Some results from the general theory of boundary value problems for PDEs

Mathematical modeling is now a universal hobby in the world. As is known, any advanced mathematical model is based on the differential equation (or a system of such equations), but in order to from a huge set of solutions select one that describes the future behavior of the modeled object, a boundary (initial) problem should be set. How to correctly set the boundary problem, properties of boundary problems and differential equations - studies the theory boundary value problems, which is currently developing only in the direction study of three types of equations and a small number of formulations of boundary value problems. What happens in the general case, for more general equations and boundary problems, studies the general theory of boundary value problems, about which little is known to the public. And this theory is evolving. Here’s about this theory and some new results author and there will be a story in my speech.