| Abstract: |
| In this talk, we present recent advancements in the mathematical analysis and control of nonlinear impulsive evolution inclusions formulated within the framework of an evolution triple of spaces. Our research focuses on a class of variational-hemivariational inequalities involving both convex and nonconvex potentials, as well as history-dependent operators. These systems represent a novel integration of impulsive effects - which introduce discontinuities and state jumps - with nonsmooth potentials described by the Clarke generalized gradient.
Using tools from nonsmooth and nonconvex analysis, specifically the Clarke generalized gradient, we establish the existence of solutions to these impulsive systems. A significant part of the presentation is devoted to an optimal control problem, where we prove the existence of optimal control-state triples under general hypotheses on the cost functional and control sets. Furthermore, we illustrate the theoretical results with applications to physical models, such as semipermeability problems and frictional contact, where surface traction is governed by impulsive differential equations. This work highlights the synergy between nonsmooth analysis, impulsive dynamics, and memory effects in solving complex problems in mechanics and physical sciences. |
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