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.
Alternative probabilistic representations of barenblatt-type solutions / De Gregorio, A.; Garra, R.. - In: MODERN STOCHASTICS: THEORY AND APPLICATIONS. - ISSN 2351-6054. - 7:1(2020), pp. 97-112. [10.15559/20-VMSTA151]
Alternative probabilistic representations of barenblatt-type solutions
De Gregorio A.
;Garra R.
2020
Abstract
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.| File | Dimensione | Formato | |
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