Geodesic
On the $n$-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group
Symmetry, integrability and geometry: methods and applications, Tome 9 (2013) Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

By restricting to a special class of smooth functions, the local action of the symmetry group is globalized. This special class of functions is constructed using parabolic induction.
Keywords: globalization; porous medium equation; Lie group representation; Lorentz group; parabolic induction. 
@article{SIGMA_2013_9_a10,
     author = {Jose A. Franco},
     title = {On the $n${-Dimensional} {Porous} {Medium} {Diffusion} {Equation} and {Global} {Actions} of the {Symmetry} {Group}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2013},
     volume = {9},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a10/}
}
TY  - JOUR
AU  - Jose A. Franco
TI  - On the $n$-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group
JO  - Symmetry, integrability and geometry: methods and applications
PY  - 2013
VL  - 9
UR  - http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a10/
LA  - en
ID  - SIGMA_2013_9_a10
ER  - 
%0 Journal Article
%A Jose A. Franco
%T On the $n$-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group
%J Symmetry, integrability and geometry: methods and applications
%D 2013
%V 9
%U http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a10/
%G en
%F SIGMA_2013_9_a10
Jose A. Franco. On the $n$-Dimensional Porous Medium Diffusion Equation and Global Actions of the Symmetry Group. Symmetry, integrability and geometry: methods and applications, Tome 9 (2013). http://geodesic.mathdoc.fr/item/SIGMA_2013_9_a10/

[1] Ames W. F., Anderson R. L., Dorodnitsyn V. A., Ferapontov E. V., Gazizov R. K., Ibragimov N. H., Svirshchevskiĭ S. R., CRC handbook of Lie group analysis of differential equations, v. 1, Symmetries, exact solutions and conservation laws, CRC Press, Boca Raton, FL, 1994 | MR

[2] Cowling M., Frenkel E., Kashiwara M., Valette A., Vogan Jr. D. A., Wallach N. R., Lectures from the C. I. M. E. Summer School (Venice, June 10–17, 2004), Lecture Notes in Mathematics, 1931, Springer-Verlag, Berlin, 2008 | DOI | MR | Zbl

[3] Craddock M. J., Dooley A. H., “On the equivalence of Lie symmetries and group representations”, J. Differential Equations, 249 (2010), 621–653 | DOI | MR | Zbl

[4] Dorodnitsyn V. A., Knyazeva I. V., Svirshchevskiĭ S. R., Group properties of the anisotropic heat equation with source $T_{t}=\sum_{i}(K_{i}(T)T_{x_{i}})_{x_{i}}+Q(T)$, Preprint No 134, Akad. Nauk SSSR Inst. Prikl. Mat., 1982, 20 pp. | MR

[5] Dos Santos Cardoso-Bihlo E., Bihlo A., Popovych R. O., “Enhanced preliminary group classification of a class of generalized diffusion equations”, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3622–3638, arXiv: 1012.0297 | DOI | MR | Zbl

[6] Franco J., “Global $\widetilde{{\rm SL}(2,R)}$ representations of the Schrödinger equation with singular potential”, Cent. Eur. J. Math., 10 (2012), 927–941, arXiv: 1104.3508 | DOI | MR | Zbl

[7] Hunziker M., Sepanski M. R., Stanke R. J., “The minimal representation of the conformal group and classical solutions to the wave equation”, J. Lie Theory, 22 (2012), 301–360, arXiv: 0901.2280 | MR | Zbl

[8] Knapp A. W., Lie groups beyond an introduction, Progress in Mathematics, 140, Birkhäuser Boston Inc., Boston, MA, 1996 | MR | Zbl

[9] Knapp A. W., Representation theory of semisimple groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 2001 | MR | Zbl

[10] Kostant B., Wallach N., Action of the conformal group on steady state solutions to Maxwell's equations and background radiation, arXiv: 1109.5745

[11] Olver P. J., Applications of {L}ie groups to differential equations, Graduate Texts in Mathematics, 107, 2nd ed., Springer-Verlag, New York, 1993 | DOI | MR | Zbl

[12] Ovsjannikov L. V., “Group relations of the equation of non-linear heat conductivity”, Dokl. Akad. Nauk SSSR, 125 (1959), 592–595 | MR

[13] Sepanski M. R., “Global actions of Lie symmetries for the nonlinear heat equation”, J. Math. Anal. Appl., 360 (2009), 35–46 | DOI | MR | Zbl

[14] Sepanski M. R., “Nonlinear potential filtration equation and global actions of Lie symmetries”, Electron. J. Differential Equations, 2009:101 (2009), 24 pp. | MR

[15] Sepanski M. R., Stanke R. J., “Global Lie symmetries of the heat and Schrödinger equation”, J. Lie Theory, 20 (2010), 543–580 | MR | Zbl

[16] Vázquez J. L., The porous medium equation. Mathematical theory, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007 | MR

[17] Wu Z., Zhao J., Yin J., Li H., Nonlinear diffusion equations, World Scientific Publishing Co. Inc., River Edge, NJ, 2001 | DOI | MR