Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type

Vázquez, Juan Luis. "Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type." Journal of the European Mathematical Society 016.4 (2014): 769-803. <http://eudml.org/doc/277593>.

@article{Vázquez2014,
abstract = {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 $u(x,t)=t^\{–\alpha \}f(|x| t^\{–\beta \})$ with suitable $$ and $\beta $. 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.},
author = {Vázquez, Juan Luis},
journal = {Journal of the European Mathematical Society},
keywords = {nonlinear fractional diffusion; fundamental solutions; very singular solutions; asymptotic behaviour; fractional Laplacian; Aleksandrov reflection principle; Barenblatt solutions; fractional Laplacian; non-linear fractional heat equation; fundamental solution; hyper-singular solutions; asymptotic behavior; Aleksandrov reflection principle; Barenblatt solutions},
language = {eng},
number = {4},
pages = {769-803},
publisher = {European Mathematical Society Publishing House},
title = {Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type},
url = {http://eudml.org/doc/277593},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Vázquez, Juan Luis
TI - Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 4
SP - 769
EP - 803
AB - 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 $u(x,t)=t^{–\alpha }f(|x| t^{–\beta })$ with suitable $$ and $\beta $. 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.
LA - eng
KW - nonlinear fractional diffusion; fundamental solutions; very singular solutions; asymptotic behaviour; fractional Laplacian; Aleksandrov reflection principle; Barenblatt solutions; fractional Laplacian; non-linear fractional heat equation; fundamental solution; hyper-singular solutions; asymptotic behavior; Aleksandrov reflection principle; Barenblatt solutions
UR - http://eudml.org/doc/277593
ER -