Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation

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A Family of Nonlinear Fourth Order Equations of Gradient Flow Type (2009, background): “1) in a way which is inspired by Carrillo and Toscani [15] and allows us to perform completely explicitly the estimates that resulted in an abstract way from the theory of gradient flows in the previous section.”
Asymptotic equipartition and long time behavior of solutions of a thin-film equation☆ (2007, background): “It was shown in previous work of Carrillo and Toscani that for non-negative initial data u0 that belongs to H 1(R) and also has a finite mass and second moment, the strong solutions relax in the L1(R) norm at an explicit rate to the unique self-similar source type solution with the same mass.”
Smooth zero-contact-angle solutions to a thin-film equation around the steady state☆ (2008, background): “[21, 9]: as a naive example, it is the only case where explicit source type self–similar solutions are known).”
The Wasserstein Gradient Flow of the Fisher Information and the Quantum Drift-diffusion Equation (2009, background): “which has been introduced by [23] and studied in a bounded domain Ω by [9] and subsequently by [33], and its (suitably) rescaled version in the whole spaceR d [ 18 ]”