%0 Generic %1 matthes2009family %A Matthes, Daniel %A McCann, Robert J. %A Savar'e, Giuseppe %D 2009 %K Gradient_Flow Optimal_Transport %T A Family of Nonlinear Fourth Order Equations of Gradient Flow Type %U http://arxiv.org/abs/0901.0540 %X 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 $Fu = 1/(2\alpha) | D (u^\alpha) |^2 dx + łambda/2 |x|^2 u dx$ with respect to the $L^2$-Wasserstein metric. The value of $\alpha$ ranges from $\alpha=1/2$, corresponding to a simplified quantum drift diffusion model, to $\alpha=1$, corresponding to a thin film type equation.

@misc{matthes2009family, 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 $F[u] = 1/(2\alpha) \int | D (u^\alpha) |^2 dx + \lambda/2 \int |x|^2 u dx$ with respect to the $L^2$-Wasserstein metric. The value of $\alpha$ ranges from $\alpha=1/2$, corresponding to a simplified quantum drift diffusion model, to $\alpha=1$, corresponding to a thin film type equation.}, added-at = {2022-11-08T16:06:55.000+0100}, author = {Matthes, Daniel and McCann, Robert J. and Savar'e, Giuseppe}, biburl = {https://www.bibsonomy.org/bibtex/2d3df4674f869366b50d1a0fa5ef78abb/fanch}, description = {A Family of Nonlinear Fourth Order Equations of Gradient Flow Type}, interhash = {e71dd3b9b11a16bf10a78e24574bff0f}, intrahash = {d3df4674f869366b50d1a0fa5ef78abb}, keywords = {Gradient_Flow Optimal_Transport}, note = {cite arxiv:0901.0540Comment: 33 pages, no figures}, timestamp = {2022-11-08T16:06:55.000+0100}, title = {A Family of Nonlinear Fourth Order Equations of Gradient Flow Type}, url = {http://arxiv.org/abs/0901.0540}, year = 2009 }