The dipole solution for the porous medium equation in several space dimensions

Josephus Hulshof; Juan Luis Vazquez

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1993)

  • Volume: 20, Issue: 2, page 193-217
  • ISSN: 0391-173X

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Hulshof, Josephus, and 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 20.2 (1993): 193-217. <http://eudml.org/doc/84146>.

@article{Hulshof1993,
author = {Hulshof, Josephus, Vazquez, Juan Luis},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Dipole solution; conservation law},
language = {eng},
number = {2},
pages = {193-217},
publisher = {Scuola normale superiore},
title = {The dipole solution for the porous medium equation in several space dimensions},
url = {http://eudml.org/doc/84146},
volume = {20},
year = {1993},
}

TY - JOUR
AU - Hulshof, Josephus
AU - Vazquez, Juan Luis
TI - The dipole solution for the porous medium equation in several space dimensions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1993
PB - Scuola normale superiore
VL - 20
IS - 2
SP - 193
EP - 217
LA - eng
KW - Dipole solution; conservation law
UR - http://eudml.org/doc/84146
ER -

References

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  2. [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. 
  3. [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. Zbl0556.35067MR648452
  4. [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, A281 (1975), 947-950. Zbl0315.35078
  5. [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. Zbl0756.35038MR1203909
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  8. [DB] E. Di Benedetto, Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math.32 (1983), 83-118. Zbl0526.35042MR684758
  9. [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. Zbl0356.35049MR436751
  10. [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. Zbl0365.35029MR436752
  11. [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. Zbl0454.35053
  12. [Ha] K.S. Ha, Sur des semigroupes non-linéaires dans les espces L∞(Ω), J. Math. Soc. Japan, 31 (1979), 593-622. Zbl0404.47038
  13. [H] J. Hulshof, Similarity solutions of the porous medium equation with sign changes, J. Math. Anal. Appl., 157 (1991), 75-111. Zbl0777.35034MR1109445
  14. [Ko] Y. Konishi, On the nonlinear semigroups associated with ut=Δβ(u) and Φ(ut)=Δu, J. Math. Soc. Japan, 25 (1973), 622-628. Zbl0259.47047
  15. [LV] A. Lacey - J.L. Vazquez, Interaction of gas fronts, Quart. Appl. Math., to appear. Zbl0759.76073MR1178428
  16. [P] Pattle, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math., 12 (1959), 407- 409. Zbl0119.30505MR114505
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