Convergence in gradient-like systems which are asymptotically autonomous and analytic

By Sen-Zhong Huang, Peter Takác. 2001

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A generalization of the Yamabe flow for manifolds with boundary (2002, methodology): “for all T ≥ t0. By Lemma 4.1 in [ 12 ], we conclude that”
Asymptotic behavior of a Cahn-Hilliard equation with Wentzell boundary conditions and mass conservation (2008, background): “We refer the reader to [18, 19, 20, 35] and the references cited therein.”
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), different arguments have been developed in the literature, we may refer to, for instance, [29,57,106,109,157,164] and also the book [105].”
Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods (2013, methodology): “Kurdyka- Lojasiewicz inequalities have been successfully used to analyze various types of asymptotic behavior: gradient-like systems [15, 33, 34, 38], PDE [52, 21], gradient methods [1, 46], proximal methods [3], projection methods or alternating methods [5, 14].”