The dipole solution for the porous medium equation in several space dimensions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 20 (1993) no. 2, pp. 193-217.
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author = {Hulshof, Josephus and Vazquez, Juan Luis},
title = {The dipole solution for the porous medium equation in several space dimensions},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {193--217},
publisher = {Scuola normale superiore},
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url = {http://www.numdam.org/item/ASNSP_1993_4_20_2_193_0/}
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Hulshof, Josephus; Vazquez, Juan Luis. The dipole solution for the porous medium equation in several space dimensions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 20 (1993) no. 2, pp. 193-217. http://www.numdam.org/item/ASNSP_1993_4_20_2_193_0/

[Ba] G.I. Barenblatt, On self-similar motions of compressible fluids in porous media, Prikl. Mat. Mekh., 16 (1952), 679-698 (in Russian). | MR | Zbl

[BZ] G.I. Barenblatt - Y.B. Zel'Dovich, On dipole-solutions in problems of nonstationary filtration of gas under polytropic regime, Prikl. Mat. Mekh., 21 (1957), 718-720.

[BC] P. Bénilan - M.G. Crandall, Regularizing effects of homogeneous evolution equations, in Contributions to Analysis and Geometry, suppl. to Amer. Math., Baltimore (1981), 23-39. | MR | Zbl

[BH] P. Bénilan - K.S. Ha, Equation d'évolution du type (du/dt)-β∂Φ(u)∈0 dans L∞(Ω), C. R. Acad. Sci. Paris, A 281 (1975), 947-950. | Zbl

[BHV] F. Bernis - J. Hulshof - J.L. Vazquez, A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions, J. reine und angewandte Math., to appear. | MR | Zbl

[CF] L.A. Caffarelli - A. Friedman, Continuity of the density of gas flow in a porous medium, Trans. Amer. Math. Soc., 252 (1979), 99-113. | MR | Zbl

[C] M.G. Crandall, An introduction to evolution governed by accretive operators, in Dynamical Systems-An International Symposium. L. Cesari, J. Hale and J. Lasalle eds., Academic Press, New York (1976), 131-165. | MR | Zbl

[DB] E. Di Benedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. 32 (1983), 83-118. | MR | Zbl

[GP1] B.H. Gilding - L.A. Peletier, On a Class of Similarity Solutions of the Porous Media Equation, J. Math. Anal. Appl., 55 (1976), 351-364. | MR | Zbl

[GP2] B.H. Gilding - L.A. Peletier, On a Class of Similarity Solutions of the Porous Media Equation II, J. Math. Anal. Appl., 57 (1977), 522-538. | MR | Zbl

[GP3] B.H. Gilding - L.A. Peletier, On a Class of Similarity Solutions of the Porous Media Equation III, J. Math. Anal. Appl., 775 (1980), 381-402. | Zbl

[Ha] K.S. Ha, Sur des semigroupes non-linéaires dans les espces L∞(Ω), J. Math. Soc. Japan, 31 (1979), 593-622. | Zbl

[H] J. Hulshof, Similarity solutions of the porous medium equation with sign changes, J. Math. Anal. Appl., 157 (1991), 75-111. | MR | Zbl

[Ko] Y. Konishi, On the nonlinear semigroups associated with ut=Δβ(u) and Φ(ut)=Δu, J. Math. Soc. Japan, 25 (1973), 622-628. | Zbl

[LV] A. Lacey - J.L. Vazquez, Interaction of gas fronts, Quart. Appl. Math., to appear. | MR | Zbl

[P] Pattle, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math., 12 (1959), 407- 409. | MR | Zbl

[S] P.E. Sacks, Continuity of solutions of a singular parabolic equation, Nonlinear Anal., 7 (1983), 387-409. | MR | Zbl

[ZK] Zel'Dovich - Kompanyeets, On the theory of heat conduction depending on temperature, Lectures dedicated on the 70th anniversary of A.F. Joffe, Akad. Nauk SSSR, (1950), 61-71 (in Russian).