Geodesic
Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 769-803

Voir la notice de l'article provenant de la source EMS Press

We establish the existence, uniqueness and main properties of the fundamental solutions for the fractional porous medium equation introduced in [51]. They are self-similar functions of the form u(x,t)=t–αf(∣x∣t–β) with suitable α and β. As a main application of this construction, we prove that the asymptotic behaviour of general solutions is represented by such special solutions. Very singular solutions are also constructed. Among other interesting qualitative properties of the equation we prove an Aleksandrov reflection principle.
DOI : 10.4171/jems/446
Classification : 26-XX, 00-XX, 35-XX, 76-XX
Keywords: Nonlinear fractional diffusion, fundamental solutions, very singular solutions, asymptotic behaviour 
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     author = {Juan Luis V\'azquez},
     title = {Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type},
     journal = {Journal of the European Mathematical Society},
     pages = {769--803},
     publisher = {mathdoc},
     volume = {16},
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     year = {2014},
     doi = {10.4171/jems/446},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/446/}
}
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Juan Luis Vázquez. Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type. Journal of the European Mathematical Society, Tome 16 (2014) no. 4, pp. 769-803. doi: 10.4171/jems/446

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