非均匀介质中具有瞬时点源的非线性辐射扩散方程的解析解
Analytic solutions of the nonlinear radiation diffusion equation with an instantaneous point source in non-homogeneous media
摘要：
本文给出了具有幂律空间密度分布的非均匀介质中具有瞬时点源的非线性辐射扩散方程的解析解。该解是均匀介质中已知解的推广。结果表明，根据空间指数的值，解决方案采取各种定性不同的形式。这些不同的形式进行了详细研究，线性和非线性热传导。此外，通过对广义解的考察，我们证明了存在空间指数的值，使得传导前沿具有恒定的速度，甚至加速。最后，各种解决方案的形式进行了详细的比较，数值模拟，并取得了很好的协议。
英文摘要：
Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known solutions for a homogeneous medium. It is shown that the solutions take various qualitatively different forms according to the value of the spatial exponent. These different forms are studied in detail for linear and non linear heat conduction. In addition, by inspecting the generalized solutions, we show that there exist values of the spatial exponent such the conduction front has constant speed or even accelerates. Finally, the various solution forms are compared in detail to numerical simulations, and a good agreement is achieved.
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