About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

First Page Preview
Filo, Ján
A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines. (English). Mathematica Slovaca, vol. 38 (1988), issue 3, pp. 273-296
MSC: 35A05, 35A35, 35K20, 35K60, 65M20 | MR 977906 | Zbl 0664.35049
References:
[1] ARONSON D. G., CRANDALL M. G., PELETIER L. A.: Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear Analysis, 6, 1982, 1001-1022. MR 0678053 | Zbl 0518.35050
[2] CHZHOU YUI-LIN: The boundary-value problems for the nonlinear parabolic equations. Mat. sb., T47(89), 4, 1959, (Russian).
[3] FILO J.: On solutions of a perturbed fast diffusion equation. Aplikace Matematiky 32, 1987, 364-380. MR 0909544 | Zbl 0652.35064
[4] FRIEDMAN A.: Partial differential equations. Holt, Rinehart and Winston, New York, 1969. MR 0445088 | Zbl 0224.35002
[5] FUČÍK S., KUFNER A.: Nonlinear differential equations. SNTL, Praha 1978 (Czech). Zbl 0474.35001
[6] JEROME J. W.: Horizontal line analysis of the multidimensional porous medium equation: existence, rate of convergence and maximum principle. Lecture Notes in Math. 506, Springer 1976. MR 0468239
[7] KAČUR J.: Method of Rothe in Evolution Equations. Teubner-Texte zur Mathematik, 80, Leipzig 1985. MR 0834176 | Zbl 0582.65084
[8] KAČUR J.: Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions. Math. Slovaca, 30, 1980, 213-237. MR 0587248 | Zbl 0452.35060
[9] KAČUR J.: On boundedness of weak solution for some class of quasilinear partial difìerential equations. Čas. pěst. matem. 98, 1973, 43-55. MR 0316889
[10] KUFNER A., JOHN O., FUČÍK S.: Function Spaces. Academia, Praha 1977. MR 0482102
[11] LADYŽENSKAJA O. A., SOLONIKOV V. A., URAĽCEVA N. N.: Linear and quasilinear equations of parabolic type. Nauka, Moscow 1967 (Russian).
[12] MADDALENA L.: Existence of global solutions for reaction-diffusion systems with density dependent diffusion. Nonlinear Analysis 8, 1984, 1383-1394. MR 0764918
[13] OLEJNIK O. A., KALASHNIKOV A. S., CHZHOU YUI-LIN: The Cauchy problem and boundary problems for equations of the type of nonstationary filtration. Izv. Akad. Nauk SSSR, Ser. Mat., 22, 1958, 667-704 (Russian). MR 0099834
[14] SABININA E. S.: On a class of quasilinear parabolic equations not solvable for the time derivative. Sibirsk. Mat. Z., 6, 1965, 1074-1100 (Russian). MR 0190552
Partner of
EuDML logo