Ill-posed boundary value problem for mixed type system equations with two degenerate lines

摘要

In this paper, ill-posed boundary value problem is investigated for a system of partial differential equations of mixed type with two degenerate lines. To boundary value problems for equations of mixed type, problems from various fields of the natural sciences can be summarized: problems of laser physics, plasma modeling, and mathematical biology. In this paper, we prove theorems on the uniqueness and conditional stability of the solution of the problem under investigation on a set of correctness. The a priori estimate of the solution is obtained by the method of logarithmic convexity and spectral decomposition.