The Second Boundary-Value Problem for Pseudoparabolic Equations in Noncylindrical Domains

This paper is devoted to the study of the solvability of the second mixed problem in a noncylindrical domain for the nonstationary equation
$$ \operatorname {div}(k(x)\operatorname {grad}u_t)-c(x)u_t-b(x)u(x,t)=f(x,t), $$
called the pseudoparabolic equation. We prove existence and uniqueness theorems for the solution in the case of contracting (as time $t$ increases) domains.