On the solvability of spatial nonlocal boundary value problemsfor one-dimensional pseudoparabolic and pseudohyperbolic equations

In the present work we study the solvability of spatial nonlocal boundary value problems for linear one-dimensional pseudoparabolic and pseudohyperbolic equations with constant coefficients, but with general nonlocal boundary conditions by A.A. Samarsky and integral conditions with variables coefficients. 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.

pseudoparabolic equation, pseudohyperbolic equation, Sobolev space, initial-boundary value problem, Fourier’s method, regular solution, integral equation of Volterra