一类非线性四阶梯度流方程
A Family of Nonlinear Fourth Order Equations of Gradient Flow Type
摘要：
研究了一类非线性四阶发展方程在$R^d$上解的整体存在性和长时间性态。这些方程构成扰动信息泛函$F[u] = 1/(2α) \int | D (u^α) |^2 dx + λ/2 \int |x|^2 u dx$关于$L^2$ -Wasserstein度量的梯度流。$α$的值的范围从对应于简化量子漂移扩散模型的$α=1/2$到对应于薄膜型方程的$α=1$。
英文摘要：
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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