论文标题
Barenblatt型解决方案的替代概率表示
Alternative probabilistic representations of Barenblatt-type solutions
论文作者
论文摘要
概率密度的一般类别的功能\ [U（x，t）= ct^{ - αd} \ left（1- \ left（\ frac {\ | x \ |} {ct^α} \ right）例如，在非线性热方程式的研究中，产生的Barenblatt溶液。提出了Barenblatt型解决方案$ U（X，T）$的替代概率表示。在一维情况下，通过这种方法，$ u（x，t）$可以与波传播相连。
A general class of probability density functions \[u(x,t)=Ct^{-αd}\left (1-\left (\frac{\|x\|}{ct^α}\right )^β\right )_+^γ,\quad x\in \mathbb{R}^d,t>0,\] is considered, containing as particular case the Barenblatt solutions arising, for instance, in the study of nonlinear heat equations. Alternative probabilistic representations of the Barenblatt-type solutions $u(x,t)$ are proposed. In the one-dimensional case, by means of this approach, $u(x,t)$ can be connected with the wave propagation.
