| Title:
|
On solutions of a perturbed fast diffusion equation (English) |
| Author:
|
Filo, Ján |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
32 |
| Issue:
|
5 |
| Year:
|
1987 |
| Pages:
|
364-380 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Slovak |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
homogeneous Dirichlet boundary conditions |
| Keyword:
|
initial distribution |
| Keyword:
|
existence |
| Keyword:
|
global solution |
| Keyword:
|
global Lipschitz continuity |
| Keyword:
|
smooth initial data |
| Keyword:
|
blow-up |
| Keyword:
|
local existence |
| Keyword:
|
finite extinction |
| Keyword:
|
nonlinear diffusion |
| Keyword:
|
method of lines |
| MSC:
|
35B40 |
| MSC:
|
35K20 |
| MSC:
|
35K55 |
| MSC:
|
35K60 |
| MSC:
|
35K65 |
| idZBL:
|
Zbl 0652.35064 |
| idMR:
|
MR0909544 |
| DOI:
|
10.21136/AM.1987.104268 |
| . |
| Date available:
|
2008-05-20T18:33:04Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104268 |
| . |
| Reference:
|
[1] D. G. Aronson M. G. Crandall L. A. Peletier: Stabilization of solutions of a degenerate nonlinear diffusion problem.Nonlinear Analysis, 6 (1982), 1001-1022. MR 0678053, 10.1016/0362-546X(82)90072-4 |
| Reference:
|
[2] P. Benilan M. K. Crandall: The continuous dependence on $\varphi$ of solutions of $u_t - \Delta \varphi (u) = = 0$.Indiana Univ. Math. J., Vol. 30, 2 (1981), 161-177. MR 0604277, 10.1512/iumj.1981.30.30014 |
| Reference:
|
[3] J. G. Berryman C. J. Holland: Stability of the separable solution for fast diffusion.Arch. Ratl. Mech. Anal., 74 (1980), 379-388. MR 0588035, 10.1007/BF00249681 |
| Reference:
|
[4] J. Filo: A nonlinear diffusion equation with nonlinear boundary conditions: method of lines.(to appear). Zbl 0664.35049, MR 0977906 |
| Reference:
|
[5] A. Friedman: Partial differential equations.Holt, Rinehart and Winston, New York, 1969. Zbl 0224.35002, MR 0445088 |
| Reference:
|
[6] S. Fučík A. Kufner: Nonlinear differential equations.SNTL, Praha 1978 (Czech). |
| Reference:
|
[7] J. W. Jerome: Horizontal line analysis of the multidimensional porous medium equation: existence, rate of convergence and maximum principles.Lecture Notes in Math. 506, Springer 1976. MR 0468239 |
| Reference:
|
[8] J. Kačur: Method of Rothe in Evolution Equations.Teubner-Texte zur Mathematik, 80, Leipzig, 1985. MR 0834176 |
| Reference:
|
[9] A. Kufner S. Fučík O. John: Function Spaces.Academia, Praha 1977. MR 0482102 |
| Reference:
|
[10] O. A. Ladyženskaja V. A. Solonikov N. N. Uraľceva: Linear and quasilinear equations of parabolic type.Nauka, Moscow 1967 (Russian). |
| Reference:
|
[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. Zbl 0563.35038, MR 0737351 |
| Reference:
|
[12] M. H. Protter H. F. Weinberger: Maximum principles.Prentice-Hall, 1967. MR 0219861 |
| Reference:
|
[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). MR 0190552 |
| Reference:
|
[14] M. E. Gurtin R. C. MacCamy: On the diffusion of biological populations.Math. Biosciences, 33 (1977), 35-49. MR 0682594, 10.1016/0025-5564(77)90062-1 |
| . |
