Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on the d-dimensional euclidean space are studied. Among them, for suitable values of the parameters we obtain a quantum drift diffusion model, and a thin film type equation. These equations constitute gradient flows for the perturbed information functionals with respect to the L^2-Wasserstein metric.

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

SAVARE', GIUSEPPE
2009-01-01

Abstract

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on the d-dimensional euclidean space are studied. Among them, for suitable values of the parameters we obtain a quantum drift diffusion model, and a thin film type equation. These equations constitute gradient flows for the perturbed information functionals with respect to the L^2-Wasserstein metric.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/203073
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