Alternative probabilistic representations of barenblatt-type solutions
A general class of probability density functions (1 (‖x‖) )γ β u(x, t) = Ct−αd − ctα, x ∈ Rd,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.