# A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

created by savare on 12 Jan 2009

[BibTeX]

Submitted Paper

Inserted: 12 jan 2009

Year: 2009

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 $$\frac1{2\alpha} \int{Rd} \big D u\alpha\big 2 \,dx + \frac\lambda2 \int{Rd} x 2 u\,dx$$ with respect to the $L^2$-Wasserstein metric. The value of $\alpha$ ranges from $1/2$, corresponding to a simplified quantum drift diffusion model, to $1$, corresponding to a thin film type equation.