论文标题
一些高阶进化方程的复发公式
Recurrence formula for some higher order evolution equations
论文作者
论文摘要
Riccati的微分方程在有限或无限的尺寸Banach空间中被配制为抽象方程。由于带有Cole-Hopf变换的Riccati的微分方程显示了一阶进化方程与二阶进化方程之间的关系，因此其概括表明存在复发公式的存在，从而导致具有不同顺序的微分方程的顺序。总而言之，通过对数的对数表示，一阶进化方程与高阶进化方程之间的转换。给出了具有不同顺序的几类进化方程，其中一些作为示例显示。
Riccati's differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati's differential equation with the Cole-Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. %%% In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.
