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 $$ \frac1{2\alpha} \int_{R^d} \big
D u^\alpha\big
2 \,dx + \frac\lambda2 \int_{R^d}
x
2 u\,dx $$ 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:

• MMS2009.pdf