Higher-order parabolic variational inequality in unbounded domains

We prove the existence and uniqueness of a solution of a nonlinear parabolic variational inequality in an unbounded domain without conditions at infinity. In particular, the initial data may infinitely increase at infinity, and a solution of the inequality is unique without any restrictions on its behavior at infinity. Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 949–968, July, 2008.