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arXiv · 0901.0540

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

Daniel Matthes·Robert J. McCann·Giuseppe Savar'e
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Abstract

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on $R^d$ are studied. These equations constitute gradient flows for the perturbed information functionals $F[u] = 1/(2α) \int | D (u^α) |^2 dx + λ/2 \int |x|^2 u dx$ with respect to the $L^2$-Wasserstein metric. The value of $α$ ranges from $α=1/2$, corresponding to a simplified quantum drift diffusion model, to $α=1$, corresponding to a thin film type equation.

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Daniel Matthes, Robert J. McCann, Giuseppe Savar'e. 2009-01-05. A Family of Nonlinear Fourth Order Equations of Gradient Flow Type. https://arxiv.org/abs/0901.0540

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