Global behaviour of solutions to some nonlinear diffusion equations
Fila, Marek ; Filo, Ján
Czechoslovak Mathematical Journal, Tome 40 (1990), p. 226-238 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1990-01-01
Classification:  35B05,  35K60 
@article{102377,
     author = {Marek Fila and J\'an Filo},
     title = {Global behaviour of solutions to some nonlinear diffusion equations},
     journal = {Czechoslovak Mathematical Journal},
     volume = {40},
     year = {1990},
     pages = {226-238},
     zbl = {0719.35041},
     mrnumber = {1046291},
     language = {en},
     url = {http://dml.mathdoc.fr/item/102377}
}

Fila, Marek; Filo, Ján. Global behaviour of solutions to some nonlinear diffusion equations. Czechoslovak Mathematical Journal, Tome 40 (1990) pp. 226-238. http://gdmltest.u-ga.fr/item/102377/

Alikakos N. D. $L^p$ bounds of solutions of reaction-diffusion equations, Comm. Partial Differential Equations 4 (1979), 827-868. (1979) | Article | MR 0537465

Aronson D. G.; Crandall M. G.; Peletier L. A. Stabilization of solutions of a degenerate nonlinear diffusion problem, , Nonlinear Analysis 6 (1982), 1001 - 1022. (1982) | Article | MR 0678053 | Zbl 0518.35050

Ball J. M. Remarks on blow-up and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford 28 (1977), 473-486. (1977) | Article | MR 0473484 | Zbl 0377.35037

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. (1978) | MR 0604277

Fila M.; Filo J. Stabilization of solutions of certain one-dimensional degenerate diffusion equations, Mathematica Slovaca 37 (1987), 217-229. (1987) | MR 0899439 | Zbl 0619.35064

Fila M.; Filo J. A blow-up result for nonlinear diffusion equations, Mathematica Siovaca 39(1989),331-346. (1989) | MR 1016350 | Zbl 0704.35071

Filo J. On solutions of perturbed fast diffusion equation, Aplikace Matematiky 32 (1987), 364-380. (1987) | MR 0909544

Friedman A. Partial Differential Equations, Holt, Rinehart and Winston, New York 1969. (1969) | MR 0445088 | Zbl 0224.35002

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). (1981) | MR 0616920

Langlais M.; Phillips D. Stabilization of solutions of nonlinear and degenerate evolution equations, Nonlinear Analysis 9 (1985), 321 - 333. (1985) | Article | MR 0783581 | Zbl 0583.35059

Levine H. A.; Sacks P. E. Some existence and nonexistence theorems for solutions of degenerate parabolic equations, J. Differential Equations 52 (1984), 135-161. (1984) | Article | MR 0741265 | Zbl 0487.34003

Lions P. L. Asymptotic behavior of some nonlinear heat equations, Physica D5 (1982), 293-306. (1982) | MR 0680566

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. (1983) | MR 0737351

Nakao M. $L^p$-estimates of solutions of some nonlinear degenerate diffusion equations, J. Math. Soc. Japan 37 (1985), 41-63. (1985) | Article | MR 0769776 | Zbl 0584.65073

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. (1984) | Article | MR 0756548 | Zbl 0565.35053

Payne L. E.; Sattinger D. H. Saddle points and instability of nonlinear hyperbolic equations, Israel J. Math. 22 (1975), 273-303. (1975) | Article | MR 0402291

Sacks P. E. Continuity ofsolutions ofa singular parabolic equation, Nonlinear Analysis 7 (1983), 387-409. (1983) | Article | MR 0696738

Sacks P. E. Global behavior for a class of nonlinear evolution equations, SIAM J. Math. Anal. 16 (1985). (1985) | Article | MR 0777465 | Zbl 0572.35062

Tsutsumi M. Existence and nonexistence of global solutions for nonlinear parabolic equations, Publ. R.I.M.S., Kyoto Univ. 8 (1972/73), 211 - 229. (1972) | Article | MR 0312079 | Zbl 0248.35074