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.
Keywords: Fisher information, Wasserstein distance, entropy, Gradient flows, minimizing movements, Thin film equation, Asymptotic decay, Second order logarithmic-Sobolev inequalities
Download: