A new approach to initial traces in nonlinear filtration

D. Andreucci; E. Di Benedetto

Annales de l'I.H.P. Analyse non linéaire (1990)

  • Volume: 7, Issue: 4, page 305-334
  • ISSN: 0294-1449

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Andreucci, D., and Di Benedetto, E.. "A new approach to initial traces in nonlinear filtration." Annales de l'I.H.P. Analyse non linéaire 7.4 (1990): 305-334. <http://eudml.org/doc/78226>.

@article{Andreucci1990,
author = {Andreucci, D., Di Benedetto, E.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {supremum-estimates; Harnack-type inequalities; initial traces; gradient averages},
language = {eng},
number = {4},
pages = {305-334},
publisher = {Gauthier-Villars},
title = {A new approach to initial traces in nonlinear filtration},
url = {http://eudml.org/doc/78226},
volume = {7},
year = {1990},
}

TY - JOUR
AU - Andreucci, D.
AU - Di Benedetto, E.
TI - A new approach to initial traces in nonlinear filtration
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1990
PB - Gauthier-Villars
VL - 7
IS - 4
SP - 305
EP - 334
LA - eng
KW - supremum-estimates; Harnack-type inequalities; initial traces; gradient averages
UR - http://eudml.org/doc/78226
ER -

References

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  2. [2] G.I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Meh., t. 16, 1952, p. 67-78. Zbl0049.41902MR46217
  3. [3] Ph. Bènilan, M.G. Crandall, M. Pierre, Solutions of the porous medium equation in RN under optimal conditions on initial values, Indiana Univ. Math. J., # 33, 1984, p. 51-87. Zbl0552.35045MR726106
  4. [4] CHEN Ya-zhe, Hölder estimates for solutions of uniformly degenerate quasilinear parabolic equations, Chin. Ann. Math., t. 5B, 4, 1984, p. 661-678. Zbl0562.35051MR795474
  5. [5] E. Dibenedetto, Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations, Arch. for Rat. Mech. Anal., t. 100, # 2, 1988, p. 129-147. Zbl0708.35017MR913961
  6. [6] E. Dibenedetto, A. Friedman, Hölder estimates for non-linear degenerate parabolic systems, J. Reine Math., t. 357, 1985, p. 1-22. Zbl0549.35061MR783531
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  8. [8] B.E.J. Dahlberg, C.E. Kenig, Non negative solutions of generalized porous medium equations, Revista Mat. Iberoamericana, t. 2, # 3, 1986, p. 267-305. Zbl0644.35057MR908054
  9. [9] N.V. Krylov, M.V. Safonov, A certain property of solutions of parabolic equations with measurable coefficients, Math. USSR Izvestijia, vol. 16, 1981, # 1, p. 151-164. Zbl0464.35035
  10. [10] M. Pierre, Uniqueness of the solutions of ut - Δφ(u) = 0 with initial datum a measure, Nonlin. Anal. TMA, vol. 6, # 2, 1987, p. 175-187. Zbl0484.35044MR651699
  11. [11] O.A. Ladyzenskaja, V.A. Solonnikov, N.N. Ural'tzeva, Linear and quasilinear equations of parabolic type, Transl. Math. Mans., vol. 23AMS, Providence, R. I., 1968. 
  12. [12] R.E. Pattle, Diffusion from an instantaneous point source with a concentration dependent coefficient, Quarterly J. Appl. Math., t. 12, 1959, p. 407-409. Zbl0119.30505MR114505
  13. [13] M.V. Safonov, The Harnack inequality for elliptic equations and the Hölder continuity of their solutions, Boundary problems of mathematical physics and adjacent questions in the theory of functions, Zap. Nauchn. Sem. Leningrad Otdel. Math. Inst. Steklov, LOMI, t. 96, 1980, p. 272-287; Engl. Transl. J. Soviet Math., LOMI, t. 20, 1983, p. 851-863. Zbl0458.35028MR579490
  14. [14] E.B. Sabinina, On the Cauchy problem for the equation of non-stationary gas filtration in several space variables, Dokl. A. N. SSSR, vol. 136, # 5, 1961, p. 1034-1037. Zbl0101.21101
  15. [15] Chen Ya-Zhe, E. Dibenedetto, On the local behaviour of solutions of singular parabolic equations, Arch. Rat. Mech. Anal., t. 103, # 4, 1988, p. 319-345. Zbl0673.35047MR955531

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