Open AccessA generalized solution of a modified Cauchy problem of class R 2 for a hyperbolic equation of the second kind
Author(s) -
Akmal Abdullayev,
K Zhuvanov,
Kudrat Ruzmetov
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1889/2/022121
Subject(s) - hyperbolic partial differential equation , mathematics , elliptic partial differential equation , cauchy problem , cauchy boundary condition , initial value problem , boundary value problem , mathematical analysis , partial differential equation , cauchy distribution , class (philosophy) , type (biology) , free boundary problem , computer science , ecology , biology , artificial intelligence
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.