Pseudoparabolic and pseudohyperbolic equations in noncylindrical time domains

We study solvability of new boundary value problems for pseudoparabolic and pseudohyperbolic equations with one spatial variable. The solutions for these problems are sought in domains noncylindrical along the time variable, not in the domains with curvilinear borders (domains with moving border) as in the previous works. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives, required in the equation, in the inner subdomains.