HISTORY OF BOUNDARY-TERM PROBLEMS FOR MIXED-TYPE EQUATIONS

Abstract

Boundary value problems for mixed-type differential equations are of great importance in mathematical physics and engineering calculations. This direction began to take shape in the late 19th and early 20th centuries and developed with the help of classical and modern mathematical analysis methods. At the initial stage of research, scientists such as E. Hopf, A. N. Kolmogorov, J. D. Tamarkin made important contributions. Mixed-type equations are used to describe quasilinear and nonlinear phenomena, which allows for in-depth study of physical processes. Modern research is focused on methods for solving these problems using numerical and analytical methods. This article discusses the historical development of boundary value problems for mixed-type equations and their current significance.