2020/01/01 by Alessandro De Gregorio, Roberto Garra
Engineering · Mathematics · Physics and Astronomy · #Class (philosophy) #Imprecise probability #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #Nonlinear system #Probabilistic logic #Probabilistic relevance model #Probability density function #Probability distribution #Statistical model #Thermoelastic and Magnetoelastic Phenomena #math.PR
paper · pdf · doi:10.15559/20-vmsta151
published as Modern Stochastics: Theory and Applications 2020, Vol. 7, No. 1, 97-112 · Published at https://doi.org/10.15559/20-VMSTA151 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)
openalex publication_date 2020/01/01 · arxiv created 2020/03/27 · arxiv updated 2020/03/30 · openalex created_date 2020/04/03 · openalex updated_date 2026/08/05
A general class of probability density functions u(x,t)=Ct-α d(1-(\frac‖ x‖ ctα )β )+γ ,\hspace1emx∈ ℝd,tgt;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.