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.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 949–968, July, 2008.
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Medvid’, I.M. Higher-order parabolic variational inequality in unbounded domains. Ukr Math J 60, 1114–1135 (2008). https://doi.org/10.1007/s11253-008-0117-5
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DOI: https://doi.org/10.1007/s11253-008-0117-5