A generalized solution of a modified Cauchy problem of class R 2 for a hyperbolic equation of the second kind

Abstract

Abstract One of the main problems in the theory of partial differential equations is the study of equations of mixed type. the modified Cauchy problem for some values of α is stated and investigated. The equations of the mixed type began to be studied systematically, after FI Frankl indicated their applications to the problems of transonic and supersonic gas dynamics. In this regard, the purpose of this work was to find out whether it is possible to find a more convenient form of representation of the solution of the Cauchy problem for a differential equation, with the help of which it would be possible to solve boundary value problems for a mixed type equation of both parabolic-hyperbolic and elliptic-hyperbolic types. The modified Cauchy problem for some values of α is stated and investigated. A convenient representation of the generalized solution of the modified Cauchy problem is obtained.