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Uniqueness of solutions of the parabolic variational inequality with variable exponent of nonlinearity. (English) Zbl 1162.35399

Summary: New properties of variable exponent Lebesgue and Sobolev spaces were examined. Using these properties we prove that the solution of some parabolic variational inequality is unique with the given conditions.

MSC:

35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
49J40 Variational inequalities
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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