Global behaviour of solutions to some nonlinear diffusion equations
Czechoslovak Mathematical Journal, Tome 40 (1990) no. 2, pp. 226-238
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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DOI : 10.21136/CMJ.1990.102377
Classification : 35B05, 35K60
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Fila, Marek; Filo, Ján. Global behaviour of solutions to some nonlinear diffusion equations. Czechoslovak Mathematical Journal, Tome 40 (1990) no. 2, pp. 226-238. doi: 10.21136/CMJ.1990.102377

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

[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. | DOI | MR | Zbl

[3] Ball J. M.: Remarks on blow-up and nonexistence theorems for nonlinear evolution equations. Quart. J. Math. Oxford 28 (1977), 473-486. | DOI | MR | Zbl

[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

[5] Fila M., Filo J.: Stabilization of solutions of certain one-dimensional degenerate diffusion equations. Mathematica Slovaca 37 (1987), 217-229. | MR | Zbl

[6] Fila M., Filo J.: A blow-up result for nonlinear diffusion equations. Mathematica Siovaca 39(1989),331-346. | MR | Zbl

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

[8] Friedman A.: Partial Differential Equations. Holt, Rinehart and Winston, New York 1969. | MR | Zbl

[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

[10] Langlais M., Phillips D.: Stabilization of solutions of nonlinear and degenerate evolution equations. Nonlinear Analysis 9 (1985), 321 - 333. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

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

[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

[14] Nakao M.: $L^p$-estimates of solutions of some nonlinear degenerate diffusion equations. J. Math. Soc. Japan 37 (1985), 41-63. | DOI | MR | Zbl

[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. | DOI | MR | Zbl

[16] Payne L. E., Sattinger D. H.: Saddle points and instability of nonlinear hyperbolic equations. Israel J. Math. 22 (1975), 273-303. | DOI | MR

[17] Sacks P. E.: Continuity ofsolutions ofa singular parabolic equation. Nonlinear Analysis 7 (1983), 387-409. | DOI | MR

[18] Sacks P. E.: Global behavior for a class of nonlinear evolution equations. SIAM J. Math. Anal. 16 (1985). | DOI | MR | Zbl

[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. | DOI | MR | Zbl

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