The second boundary-value problem for pseudoparabolic equations in noncylindrical domains (Q1810159)

The authors study the question of the existence and uniqueness of the solution of the pseudoparabolic equation \[ \text{div}(k(x)\text{grad }u_t)- c(x) u_t= b(x) u(x,t)+ f(x,t), \] in a noncylindrical domain. They prove existence and uniqueness theorems for the solutions in the case of contracting in time (as time \(t\) increases) domains for the second mixed problem.