| Abstract: |
| Stability analysis of differential inclusions governed by maximally monotone operators presents significant challenges, especially when focusing on sets rather than isolated equilibria. Traditional methods often require explicit solutions or specific assumptions that may not be feasible. This talk addresses these issues by exploring pointwise asymptotic stability (PAS) and semistability. The approach involves splitting the operator into a convex upper-semicontinuous (CUSCO) mapping and a normal cone, simplifying the problem and allowing for a thorough examination of stability. By using nonsmooth Lyapunov pairs and proximal analysis, this method avoids many traditional assumptions, making the results more widely applicable. This framework extends stability analysis to a broader range of dynamic systems, even when explicit solutions are not available. |
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