论文标题
空间和时空部分偏微分方程的最大原理
Maximum principle for space and time-space fractional partial differential equations
论文作者
论文摘要
在本文中，我们获得了函数在其极点点的顺序Caputo分数衍生物的新估计。我们得出了线性分数方程的比较原理，并应用这些原理以获得线性和非线性分数微分方程溶液的下限和上限。然后，将极端原理应用于表明非线性异常扩散的初始界价问题最多具有一个经典解决方案，并且该解决方案不断取决于初始和边界数据。这对卢奇科（Luchko）在2011年提出的空间和时间空间分数PDE的最大原理的开放问题积极回答。还证明了具有分数衍生物和分数拉普拉斯方程的椭圆方程的极值原理。
In this paper we obtain new estimates of the sequential Caputo fractional derivatives of a function at its extremum points. We derive comparison principles for the linear fractional differential equations, and apply these principles to obtain lower and upper bounds of solutions of linear and nonlinear fractional differential equations. The extremum principle is then applied to show that the initial-boundary-value problem for nonlinear anomalous diffusion possesses at most one classical solution and this solution depends continuously on the initial and boundary data. This answers positively to the open problem about maximum principle for the space and time-space fractional PDEs posed by Luchko in 2011. The extremum principle for an elliptic equation with a fractional derivative and for the fractional Laplace equation are also proved.
