Gradient Inequalities: With Applications to Asymptotic Behavior And Stability of Gradient-like Systems

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A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “To achieve such a goal (not limited to the Cahn–Hilliard equation but also for other gradient-like systems), di ff erent arguments have been developed in the literature, we may refer to, for instance, [77,94,120,121] and the references cited therein.”
Characterizations of Lojasiewicz inequalities and applications (2008, background): “Many results related to partial differential equations followed, see the monograph of Huang [27] for an insight.”
Characterizations of Lojasiewicz inequalities: Subgradient flows, talweg, convexity (2009, background): “a K L–type inequality are called gradient dominated functions), and partial differential equations [51, 35, 30, 31], we hereby tackle the problem of characterizing such inequalities in a nonsmooth infinite-dimensional setting and provide further clarifications for several application aspects.”
Fast optimization via inertial dynamics with closed-loop damping (2020, methodology): “We refer to Barta–Chill–Fašangová [38], [39], [56], Chergui [55], Huang [66] and the references therein for further geometrical insights on the topic.”
Lyapunov functions and convergence to steady state for differential equations of fractional order (2008, unknown): “[3], [5], [10], [13], [15], [20], and the references given therein.”