M. D. P. Monteiro Marques

Degenerate Sweeping Processes

The aim of this paper is to summarize some recent results concerning the evolutionary differential inclusions {fy(1)|31-1} where A is a maximal monotone and strongly monotone operator in a real Hilbert space H, and t →C(t) is a set-valued mapping, cf. the precise assumptions below. Moreover, as usually, denotes the cone of normals to the closed convex set C(t) at the point v G C(t).

Second-Order Evolution Problems with Time-Dependent Maximal Monotone Operator and Applications

We consider at first the existence and uniqueness of solution for a general second-order evolution inclusion in a separable Hilbert space of the form

Genericity and existence of a minimum for scalar integral functionals

\displaystyle 0\in \ddot u(t) + A(t) \dot u(t) + f(t, u(t)), \hskip 2pt t\in [0, T]

On the stability of quasi-static paths for finite dimensional elastic-plastic systems with hardening

where A(t) is a time dependent with Lipschitz variation maximal monotone operator and the perturbation f(t, .) is boundedly Lipschitz. Several new results are presented in the sense that these second-order evolution inclusions deal with time-dependent maximal monotone operators by contrast with the classical case dealing with some special fixed operators. In particular, the existence and uniqueness of solution to

Dynamics with friction and persistent contact

\displaystyle 0= \ddot u(t) + A(t) \dot u(t) + \nabla \varphi (u(t)), \hskip 2pt t\in [0, T]

Perturbed Evolution Problems with Continuous Bounded Variation in Time and Applications

where A(t) is a time dependent with Lipschitz variation single-valued maximal monotone operator and ∇φ is the gradient of a smooth Lipschitz function φ are stated. Some more general inclusion of the form