非线性广义分数阶热波方程的渐近解

Asymptopic solution to nonlinear generalized fractional order thermal wave equation

研究了一类非线性广义热波方程.首先在简化的热波方程情形下求得解,其次用泛函分析同伦映射方法,求出了广义非线性扰动热波方程初始-边值问题任意次的渐近解.并举例求得了其渐近解以及解的精度.最后简述了它的物理意义.并说明了它是近似的解析解,弥补了单纯用数值方法模拟解的不足.

A class of nonlinear generalized thermal wave equation was considered.Firstly,the solution to reduced thermal wave equation was obtained.Next,the arbitrary order asymptopic solutions to generalized nonlinear disturbed thermal wave equation initial-boundary value problem were constructed by using the method of functional analysis homotopic mapping.An example was given and the accuracy of its asymptopic solution was obtained.Finally,the physical sense of the solution was briefly stated.The approximate analysis solution makes up for the simple numerical simulation solution deficiency.