A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines

Ján Filo

Mathematica Slovaca (1988)

  • Volume: 38, Issue: 3, page 273-296
  • ISSN: 0139-9918

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Filo, Ján. "A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines." Mathematica Slovaca 38.3 (1988): 273-296. <http://eudml.org/doc/34275>.

@article{Filo1988,
author = {Filo, Ján},
journal = {Mathematica Slovaca},
keywords = {Existence; uniqueness; weak solutions; method of lines; smoothness; growth},
language = {eng},
number = {3},
pages = {273-296},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines},
url = {http://eudml.org/doc/34275},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Filo, Ján
TI - A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines
JO - Mathematica Slovaca
PY - 1988
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 38
IS - 3
SP - 273
EP - 296
LA - eng
KW - Existence; uniqueness; weak solutions; method of lines; smoothness; growth
UR - http://eudml.org/doc/34275
ER -

References

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  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. (1982) Zbl0518.35050MR0678053
  2. CHZHOU YUI-LIN, The boundary-value problems for the nonlinear parabolic equations, Mat. sb., T47(89), 4, 1959, (Russian). (1959) 
  3. FILO J., On solutions of a perturbed fast diffusion equation, Aplikace Matematiky 32, 1987, 364-380. (1987) Zbl0652.35064MR0909544
  4. FRIEDMAN A., Partial differential equations, Holt, Rinehart and Winston, New York, 1969. (1969) Zbl0224.35002MR0445088
  5. FUČÍK S., KUFNER A., Nonlinear differential equations, SNTL, Praha 1978 (Czech). (1978) Zbl0474.35001
  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. (1976) MR0468239
  7. KAČUR J., Method of Rothe in Evolution Equations, Teubner-Texte zur Mathematik, 80, Leipzig 1985. (1985) Zbl0582.65084MR0834176
  8. KAČUR J., Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions, Math. Slovaca, 30, 1980, 213-237. (1980) Zbl0452.35060MR0587248
  9. KAČUR J., On boundedness of weak solution for some class of quasilinear partial difìerential equations, Čas. pěst. matem. 98, 1973, 43-55. (1973) MR0316889
  10. KUFNER A., JOHN O., FUČÍK S., Function Spaces, Academia, Praha 1977. (1977) MR0482102
  11. LADYŽENSKAJA O. A., SOLONIKOV V. A., URAĽCEVA N. N., Linear and quasilinear equations of parabolic type, Nauka, Moscow 1967 (Russian). (1967) 
  12. MADDALENA L., Existence of global solutions for reaction-diffusion systems with density dependent diffusion, Nonlinear Analysis 8, 1984, 1383-1394. (1984) MR0764918
  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). (1958) MR0099834
  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). (1965) MR0190552

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