# On existence of the weak solution for nonlinear diffusion equation

Applications of Mathematics (1991)

- Volume: 36, Issue: 1, page 9-20
- ISSN: 0862-7940

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topZeman, Juraj. "On existence of the weak solution for nonlinear diffusion equation." Applications of Mathematics 36.1 (1991): 9-20. <http://eudml.org/doc/15656>.

@article{Zeman1991,

abstract = {The paper concerns the existence of bounded weak solutions of a anonlinear diffusion equation with nonhomogeneous mixed boundary conditions.},

author = {Zeman, Juraj},

journal = {Applications of Mathematics},

keywords = {nonlinear diffusion; method of lines; bounded weak solutions; nonhomogeneous mixed boundary conditions; initial-boundary value problem; bounded weak solutions; nonhomogeneous mixed boundary conditions; initial-boundary value problem; nonlinear diffusion},

language = {eng},

number = {1},

pages = {9-20},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On existence of the weak solution for nonlinear diffusion equation},

url = {http://eudml.org/doc/15656},

volume = {36},

year = {1991},

}

TY - JOUR

AU - Zeman, Juraj

TI - On existence of the weak solution for nonlinear diffusion equation

JO - Applications of Mathematics

PY - 1991

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 36

IS - 1

SP - 9

EP - 20

AB - The paper concerns the existence of bounded weak solutions of a anonlinear diffusion equation with nonhomogeneous mixed boundary conditions.

LA - eng

KW - nonlinear diffusion; method of lines; bounded weak solutions; nonhomogeneous mixed boundary conditions; initial-boundary value problem; bounded weak solutions; nonhomogeneous mixed boundary conditions; initial-boundary value problem; nonlinear diffusion

UR - http://eudml.org/doc/15656

ER -

## References

top- H. W. Alt S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z. 183, 311-341 (1983). (1983) MR0706391
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- S. Fučík A. Kufner, Nonlinear Differential Equations, Amsterdam-Oxford-New Nork, Elsevier 1980. (1980) MR0558764
- J. Kačur, On boundedness of the weak solution for some class of quasilinear partial differential equations, Časopis pěst. mat. 98 (1973), 43-55. (1973) MR0316889
- J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Prague, 1967. (1967) MR0227584
- J. Filo, On solutions of a perturbed fast diffusion equation, Aplikace matematiky 32, 1987, 364-380. (1987) Zbl0652.35064MR0909544
- J. L. Lions, Quelques méthodes de résolution des problémes aux limites non linéaires, Russian translation, Moskva 1972. (1972) Zbl0248.35001
- H. Gajewski K. Gröger K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie-Verlag, Berlin, 1974. (1974) MR0636412

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