On solutions of a perturbed fast diffusion equation

Ján Filo

Aplikace matematiky (1987)

  • Volume: 32, Issue: 5, page 364-380
  • ISSN: 0862-7940

Abstract

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The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.

How to cite

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Filo, Ján. "On solutions of a perturbed fast diffusion equation." Aplikace matematiky 32.5 (1987): 364-380. <http://eudml.org/doc/15508>.

@article{Filo1987,
abstract = {The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.},
author = {Filo, Ján},
journal = {Aplikace matematiky},
keywords = {homogeneous Dirichlet boundary conditions; initial distribution; existence; global solution; global Lipschitz continuity; smooth initial data; blow-up; local existence; finite extinction; nonlinear diffusion; method of lines; homogeneous Dirichlet boundary conditions; initial distribution; existence; global solution; global Lipschitz continuity; smooth initial data; blow-up; local existence; finite extinction},
language = {eng},
number = {5},
pages = {364-380},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On solutions of a perturbed fast diffusion equation},
url = {http://eudml.org/doc/15508},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Filo, Ján
TI - On solutions of a perturbed fast diffusion equation
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 5
SP - 364
EP - 380
AB - The paper concerns the (local and global) existence, nonexistence, uniqueness and some properties of nonnegative solutions of a nonlinear density dependent diffusion equation with homogeneous Dirichlet boundary conditions.
LA - eng
KW - homogeneous Dirichlet boundary conditions; initial distribution; existence; global solution; global Lipschitz continuity; smooth initial data; blow-up; local existence; finite extinction; nonlinear diffusion; method of lines; homogeneous Dirichlet boundary conditions; initial distribution; existence; global solution; global Lipschitz continuity; smooth initial data; blow-up; local existence; finite extinction
UR - http://eudml.org/doc/15508
ER -

References

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  2. P. Benilan M. K. Crandall, 10.1512/iumj.1981.30.30014, Indiana Univ. Math. J., Vol. 30, 2 (1981), 161-177. (1981) MR0604277DOI10.1512/iumj.1981.30.30014
  3. J. G. Berryman C. J. Holland, 10.1007/BF00249681, Arch. Ratl. Mech. Anal., 74 (1980), 379-388. (1980) MR0588035DOI10.1007/BF00249681
  4. J. Filo, A nonlinear diffusion equation with nonlinear boundary conditions: method of lines, (to appear). Zbl0664.35049MR0977906
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  8. J. Kačur, Method of Rothe in Evolution Equations, Teubner-Texte zur Mathematik, 80, Leipzig, 1985. (1985) MR0834176
  9. A. Kufner S. Fučík O. John, Function Spaces, Academia, Praha 1977. (1977) MR0482102
  10. O. A. Ladyženskaja V. A. Solonikov N. N. Uraľceva, Linear and quasilinear equations of parabolic type, Nauka, Moscow 1967 (Russian). (1967) 
  11. M. Nakao, Existence, nonexistence and some asymptotic behaviour of global solutions of a nonlinear degenerate parabolic equation, Math. Rep. College of Gen. Edc., Kyushu Univ. 14(1983), 1-21. (1983) Zbl0563.35038MR0737351
  12. M. H. Protter H. F. Weinberger, Maximum principles, Prentice-Hall, 1967. (1967) MR0219861
  13. E. S. Sabinina, On a class of quasilinear parabolic equations not solvable for the time derivative, Sibirsk. Mat. Z., 6 (1965), 1074-1100 (Russian). (1965) MR0190552
  14. M. E. Gurtin R. C. MacCamy, 10.1016/0025-5564(77)90062-1, Math. Biosciences, 33 (1977), 35-49. (1977) MR0682594DOI10.1016/0025-5564(77)90062-1

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