| Title:
|
Global behaviour of solutions to some nonlinear diffusion equations (English) |
| Author:
|
Fila, Marek |
| Author:
|
Filo, Ján |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1990 |
| Pages:
|
226-238 |
| . |
| Category:
|
math |
| . |
| MSC:
|
35B05 |
| MSC:
|
35K60 |
| idZBL:
|
Zbl 0719.35041 |
| idMR:
|
MR1046291 |
| DOI:
|
10.21136/CMJ.1990.102377 |
| . |
| Date available:
|
2008-06-09T15:32:35Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102377 |
| . |
| Reference:
|
[1] Alikakos N. D.: $L^p$ bounds of solutions of reaction-diffusion equations.Comm. Partial Differential Equations 4 (1979), 827-868. MR 0537465, 10.1080/03605307908820113 |
| Reference:
|
[2] Aronson D. G., Crandall M. G., Peletier L. A.: Stabilization of solutions of a degenerate nonlinear diffusion problem., Nonlinear Analysis 6 (1982), 1001 - 1022. Zbl 0518.35050, MR 0678053, 10.1016/0362-546X(82)90072-4 |
| Reference:
|
[3] Ball J. M.: Remarks on blow-up and nonexistence theorems for nonlinear evolution equations.Quart. J. Math. Oxford 28 (1977), 473-486. Zbl 0377.35037, MR 0473484, 10.1093/qmath/28.4.473 |
| Reference:
|
[4] Benilan P., Crandall M. G.: The continuous dependence on $\varphi $ of solutions of $u\sb{t}-\Delta \varphi (u)=0$.Indiana Univ. Math. J. 30 (1978), 161-177. MR 0604277 |
| Reference:
|
[5] Fila M., Filo J.: Stabilization of solutions of certain one-dimensional degenerate diffusion equations.Mathematica Slovaca 37 (1987), 217-229. Zbl 0619.35064, MR 0899439 |
| Reference:
|
[6] Fila M., Filo J.: A blow-up result for nonlinear diffusion equations.Mathematica Siovaca 39(1989),331-346. Zbl 0704.35071, MR 1016350 |
| Reference:
|
[7] Filo J.: On solutions of perturbed fast diffusion equation.Aplikace Matematiky 32 (1987), 364-380. MR 0909544 |
| Reference:
|
[8] Friedman A.: Partial Differential Equations.Holt, Rinehart and Winston, New York 1969. Zbl 0224.35002, MR 0445088 |
| Reference:
|
[9] Galaktionov V. A.: A boundary value problem for the nonlinear parabolic equation $u\sb{t}=\Delta u\sp{\sigma +1}+u\sp{\beta }$.Differential Equations 17 (1981), 836-842 (Russian). MR 0616920 |
| Reference:
|
[10] Langlais M., Phillips D.: Stabilization of solutions of nonlinear and degenerate evolution equations.Nonlinear Analysis 9 (1985), 321 - 333. Zbl 0583.35059, MR 0783581, 10.1016/0362-546X(85)90057-4 |
| Reference:
|
[11] Levine H. A., Sacks P. E.: Some existence and nonexistence theorems for solutions of degenerate parabolic equations.J. Differential Equations 52 (1984), 135-161. Zbl 0487.34003, MR 0741265, 10.1016/0022-0396(84)90174-8 |
| Reference:
|
[12] Lions P. L.: Asymptotic behavior of some nonlinear heat equations.Physica D5 (1982), 293-306. MR 0680566 |
| Reference:
|
[13] Nakao M.: Existence, nonexistence and some asymptotic behavior of global solutions of a nonlinear degenerate parabolic equation.Math. Rep., College Gen. Ed. Kyushu Univ., 1983, 1-21. MR 0737351 |
| Reference:
|
[14] Nakao M.: $L^p$-estimates of solutions of some nonlinear degenerate diffusion equations.J. Math. Soc. Japan 37 (1985), 41-63. Zbl 0584.65073, MR 0769776, 10.2969/jmsj/03710041 |
| Reference:
|
[15] Ni W. M., Sacks P. E., Tavantzis J.: On the asymptotic behavior of solutions of certain quasilinear parabolic equations.J. Differential Equations 54 (1984), 97-120. Zbl 0565.35053, MR 0756548, 10.1016/0022-0396(84)90145-1 |
| Reference:
|
[16] Payne L. E., Sattinger D. H.: Saddle points and instability of nonlinear hyperbolic equations.Israel J. Math. 22 (1975), 273-303. MR 0402291, 10.1007/BF02761595 |
| Reference:
|
[17] Sacks P. E.: Continuity ofsolutions ofa singular parabolic equation.Nonlinear Analysis 7 (1983), 387-409. MR 0696738, 10.1016/0362-546X(83)90092-5 |
| Reference:
|
[18] Sacks P. E.: Global behavior for a class of nonlinear evolution equations.SIAM J. Math. Anal. 16 (1985). Zbl 0572.35062, MR 0777465, 10.1137/0516018 |
| Reference:
|
[19] Tsutsumi M.: Existence and nonexistence of global solutions for nonlinear parabolic equations.Publ. R.I.M.S., Kyoto Univ. 8 (1972/73), 211 - 229. Zbl 0248.35074, MR 0312079, 10.2977/prims/1195193108 |
| . |
