Open AccessOn the solvability of spatial nonlocal boundary value problemsfor one-dimensional pseudoparabolic and pseudohyperbolic equations
Author(s) -
Н. С. Попов
Publication year - 2015
Publication title -
vestnik samarskogo universiteta. estestvennonaučnaâ seriâ
Language(s) - English
Resource type - Journals
eISSN - 2712-8954
pISSN - 2541-7525
DOI - 10.18287/2541-7525-2015-21-3-29-43
Subject(s) - mathematics , uniqueness , boundary value problem , mathematical analysis , integral equation , work (physics) , volterra integral equation , constant (computer programming) , mechanical engineering , computer science , engineering , programming language
In the present work we study the solvability of spatial nonlocal boundary value problems for linear one-dimensional pseudoparabolic and pseudohyperbolic equations with constant coecients, but with general nonlocal boundary conditions by A.A. Samarsky and integral conditions with variables coecients. The proof of the theorems of existence and uniqueness of regular solutions is carried out by the method of Fourier. The study of solvability in the classes of regular solutions leads to the study of a system of integral equations of Volterra of the second kind. In particular cases nongeneracy conditions of the obtained systems of integral equations in explicit form are given.