Hemivariational Inequalities and Hysteresis
Hemivariational inequalities introduced by P.D. Panagiotopoulos are generalizations of variational inequalities. This type of inequality problems arises, e.g. in variational formulation of mechanical problems whenever nonmonotone and multivalued relations or nonconvex energy functions are involved. Typical examples of such kind of phenomena are nonmonotone friction laws and adhesive contact laws. Mathematically these nonmonotone relations are described by means of generalized gradients (in sense of F.H. Clarke) of nonconvex potential functions. For applications and for their mathematical treatment we refer to ,,–.
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- M. Brokate and J. Sprekels. Hysteresis and Phase Transitions. Springer Verlag, New York, 1996.Google Scholar
- G. Fichera. Boundary value problems in elasticity with unilateral constraints. In: C. Truesdell, Encyclopedia of Physics VI a/2, Mechanics of Solids II, pp. 391–424. Springer Verlag, Berlin, 1972.Google Scholar
- M.A. Krasnoselskii and A.V. Pokrovskii. Systems with Hysteresis. Springer Verlag, Heidelberg, 1989.Google Scholar
- P. Krejči. Hysteresis, Convexity and Dissipation in Hyperbolic Equations Gakkotosho, Tokyo, 1996.Google Scholar
- M. Miettinen and P.D. Panagiotopoulos. On parabolic hemivariational inequalities and applications. to appear in Nonlinear Analysis.Google Scholar
- M. Miettinen and P.D. Panagiotopoulos. Hysteresis and hemivariational inequalities: Semilinear Case. to appear in J. Global Optimization.Google Scholar
- M. Miettinen and P.D. Panagiotopoulos. Hysteresis and hemivariational inequalities: Quasilinear Case. preprint.Google Scholar
- D. Motreanu and P.D. Panagiotopoulos. Double eigenvalue problems for hemivariational inequalities, to appear in Arch. Rat. Mech. Anal.Google Scholar
- Z. Naniewicz and P.D. Panagiotopoulos. Mathematical Theory of Hemivariational Inequalities and Applications. Marcel Dekker, New York, 1995.Google Scholar
- P.D. Panagiotopoulos. Hemivariational Inequalities. Applications in Mechanics and Engineering. Springer Verlag, New York, Berlin, 1993.Google Scholar