Nonsmooth Evolution Problems
In this Chapter one discusses existence, uniqueness, Lipschitz continuous dependence on initial conditions and stability of solutions for different evolution initial value problems written in the form of variational inequalities or equalities. Section 1 concerns the study of the Cauchy problem for a first order dynamical variational inequality. Section 2 contains an existence result for the solutions of a Cauchy problem for a second order evolution variational equation. In Section 3 one presents stability, asymptotic stability and unstability results for first order evolution variational inequalities.
Unable to display preview. Download preview PDF.
- B. Brogliato, Absolute stability and the Lagrange-Dirichlet theorem with monotone multivalued mappings, Internal Report, INRIA Rhônes-Alpes, 2002.Google Scholar
- C. Ciulcu, D. Motreanu and M. Sofonea, Analysis of an elastic contact problem with slip dependent coefficient of friction, Math. Inequal. Appl. 4 (2001), 465479.Google Scholar
- D. Goeleven, D. Motreanu and V. V. Motreanu, On the stability of stationary solutions of first order evolution variational inequalities, Adv. Nonlinear Var. Inequal. 6 (2003), to appear.Google Scholar
- W. Han and M. Sofonea, Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity,Studies in Advanced Mathematics, American Mathematical Society-International Press, to appear.Google Scholar
- D. Motreanu and M. Sofonea, Second order variational equations and applications in dynamic contact problems for elastic materials, preprint.Google Scholar
- K. Tsilika, Study of an adhesively supported von Krmn plate. Existence and bifurcation of the solutions, in: Nonsmooth/nonconvex mechanics (Blacksburg, VA, 1999), 411–425, Nonconvex Optim. App1. 50, Kluwer Acad. Publ., Dordrecht, 2001.Google Scholar