# On a Parabolic Variational Inequality That Generalizes the Equation of Polytropic Filtration

@article{Buhrii2001OnAP, title={On a Parabolic Variational Inequality That Generalizes the Equation of Polytropic Filtration}, author={O. M. Buhrii and S. P. Lavrenyuk}, journal={Ukrainian Mathematical Journal}, year={2001}, volume={53}, pages={1027-1042} }

- Published 2001
DOI:10.1023/A:1013368412665

We obtain conditions for the existence and uniqueness of a solution of a parabolic variational inequality that is a generalization of the equation of polytropic elastic filtration without initial conditions. The class of uniqueness of a solution of this problem consists of functions that increase not faster than e−μt, μ > 0, as t → −∞.

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## EXISTENCE AND BOUNDEDNESS OF SOLUTIONS FOR EVOLUTION VARIATIONAL INEQUALITIES WITH p(x, t)-GROWTH

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