On Fast-Diffusion Equations with Infinite Equilibrium Entropy and Finite Equilibrium Mass
On Fast-Diffusion Equations with Infinite Equilibrium Entropy and Finite Equilibrium Mass
复制标题
关于具有无限平衡熵和有限平衡质量的快速扩散方程
DOI：
10.1081/pde-120019384
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发表时间：
2003
影响因子：
1.9
通讯作者：
P. Markowich
中科院分区：
文献类型：
--
作者：
C. Lederman;P. Markowich
摘要我们将已有的对流扩散方程的大时间渐近性理论，基于熵-熵耗散方法，推广到某些具有一致凸约束势和有限质量无限熵平衡解的快扩散方程。我们证明了存在的质量保持解决方案的柯西问题，我们显示指数收敛，作为，在一个精确的速度，相应的平衡解决方案的L1规范。作为副产品，我们还得到相应的广义Sobolev不等式。
Abstract We extend the existing theory on large-time asymptotics for convection–diffusion equations, based on the entropy–entropy dissipation approach, to certain fast diffusion equations with uniformly convex confinement potential and finite-mass but infinite-entropy equilibrium solutions. We prove existence of a mass preserving solution of the Cauchy problem and we show exponential convergence, as , at a precise rate to the corresponding equilibrium solution in the L 1 norm. As by-product we also derive corresponding generalized Sobolev inequalities.