论文标题
使用hellinger距离的校正后lebowitz-speer-spohn方程的数值方案的适应性和收敛性
Well-posedness and convergence of a numerical scheme for the corrected Derrida-Lebowitz-Speer-Spohn equation using the Hellinger distance
论文作者
论文摘要
在本文中，我们构建了一个独特的全局时间弱非负解决方案，用于校正后的lebowitz-speer-spohn方程，该方程统计地描述了某个自旋系统中两个阶段之间的界面波动。弱溶液的构造是基于Lyapunov功能的耗散，该功能等于溶液和恒定稳态之间的Hellinger距离的平方。此外，结果表明，弱解在Hellinger距离中以指数级的速率收敛到恒定的稳态，从而在$ l^1 $ norm中收敛。设计了方程式的变分结构的数值方案，并在离散的地狱距离方面得到了融合。
In this paper we construct a unique global in time weak nonnegative solution to the corrected Derrida-Lebowitz-Speer-Spohn equation, which statistically describes the interface fluctuations between two phases in a certain spin system. The construction of the weak solution is based on the dissipation of a Lyapunov functional which equals to the square of the Hellinger distance between the solution and the constant steady state. Furthermore, it is shown that the weak solution converges at an exponential rate to the constant steady state in the Hellinger distance and thus also in the $L^1$-norm. Numerical scheme which preserves the variational structure of the equation is devised and its convergence in terms of a discrete Hellinger distance is demonstrated.
