Open AccessON SOLVABILITY OF NONLOCAL PROBLEM FOR THIRD-ORDER EQUATION
Author(s) -
Olga Mikhailovna KECHINA
Publication year - 2017
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2017-23-1-15-20
Subject(s) - mathematics , partial differential equation , hyperbolic partial differential equation , first order partial differential equation , order (exchange) , mathematical analysis , volterra integral equation , integro differential equation , summation equation , integral equation , domain (mathematical analysis) , differential equation , function (biology) , reduction (mathematics) , elliptic partial differential equation , geometry , finance , evolutionary biology , economics , biology
In this paper nonlocal problem with integral conditions for partial differential equation of the third order is considered. The existence of a unique classical solution is proved in rectangular domain. The proof is carried out by the method of auxiliary problems. At first the problem for a new function for partial differential equation of the first order is considered. Then the solvability of integral analogue of Goursat problem for hyperbolic equation of the second order is proved by equivalent reduction of the problem to the Volterra integral equation of the second kind.