Journal of Mathematical Sciences

, Volume 127, Issue 5, pp 2284–2314 | Cite as

Solvability of Unilateral Parabolic Problems and Variational Inequalities

  • O. V. Solonukha


Sufficient conditions are given for the existence of solutions of strong parabolic variational inequalities with nonlinear and multi-valued operators. Pseudomonotone operators are used. A new multi-valued analogue of the acute-angle lemma is used for the localization. The theory can be applied to problems with distributed parameters. We also consider conditions for the existence of strong generalized solutions of parabolic equations with unilateral boundary conditions with applications to control problems.


Boundary Condition Generalize Solution Variational Inequality Parabolic Equation Parabolic Problem 


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© Springer Science+Business Media, Inc. 2005

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  • O. V. Solonukha

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