The paper introduces distributional ISS via Wasserstein distance and proves stability for l-smooth lambda-convex Wasserstein gradient flows under bounded perturbations, plus error bounds for kernel and particle approximations.
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2026 2verdicts
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The paper demonstrates systematic construction of generalized Lyapunov functionals to obtain explicit ISS estimates in L^q spaces for nonlinear parabolic, first-order hyperbolic, and wave equations.
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Input-to-State Stability of Gradient Flows in Distributional Space
The paper introduces distributional ISS via Wasserstein distance and proves stability for l-smooth lambda-convex Wasserstein gradient flows under bounded perturbations, plus error bounds for kernel and particle approximations.
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Unified Lyapunov Method for ISS of PDEs: A Tutorial on Constructing Generalized Lyapunov Functionals for Parabolic and Hyperbolic Equations
The paper demonstrates systematic construction of generalized Lyapunov functionals to obtain explicit ISS estimates in L^q spaces for nonlinear parabolic, first-order hyperbolic, and wave equations.