×

On parabolic hemivariational inequalities and applications. (English) Zbl 0923.35089

This paper deals with parabolic hemivariational and parabolic variational-hemivariational inequalities. The authors prove existence results for problems having nonmonotone behaviour on the boundary and for problems involving convex functionals or constraints. The proofs are based on Galerkin’s method and regularization techniques.
As applications are discussed dynamic nonconvex semipermeability problems and rigid viscoplastic laminar flow problems in cylindrical pipes with adhesion or nonmonotone friction.
Reviewer: M.A.Vivaldi (Roma)

MSC:

35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
49J40 Variational inequalities
PDF BibTeX XML Cite
Full Text: DOI

References:

[2] Carl, S., Enclosure of solutions for quasilinear hemivariational parabolic problems, Nonlin. World, 3, 281-298 (1996) · Zbl 0902.35065
[3] Carl, S.; Heikkilä, S., Extremal solutions of quasilinear parabolic boundary value problems with discontinuous nonlinearities, Dyn. Systems Appl., 3, 251-258 (1994) · Zbl 0803.35077
[7] Jarusek, J., Dynamic contact problems with given friction for viscoelastic bodies, Czech. Math. J., 46, 121, 475-487 (1996) · Zbl 0879.73022
[8] Landes, R., On the existence of weak solutions for quasilinear parabolic initial-boundary problems, Proc. R. Soc. Edinb. A, 89, 217-237 (1981) · Zbl 0493.35054
[9] Landes, R., A note on strongly nonlinear parabolic equations of higher order, Diff. Integral Eqns, 3, 851-862 (1990) · Zbl 0733.35052
[10] Landes, R.; Mustonen, V., A strongly nonlinear parabolic initial value problem, Ark. f. Math., 25, 29-40 (1987) · Zbl 0697.35071
[13] Miettinen, M., A parabolic hemivariational inequality, Nonlin. Anal., 26, 725-734 (1996) · Zbl 0858.35072
[14] Naniewicz, Z., Hemivariational inequalities with functionals which are not locally Lipschitz, Nonlin. Anal., 25, 1307-1320 (1995) · Zbl 0849.49013
[17] Panagiotopoulos, P. D., Coercive and semicoercive hemivariational inequalities, Nonlin. Anal., 16, 209-231 (1991) · Zbl 0733.49012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.