Higher-order parabolic variational inequality in unbounded domains - Medvid’, I. M. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
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.