# On iterative solution of nonlinear heat-conduction and diffusion problems

Aplikace matematiky (1977)

- Volume: 22, Issue: 2, page 77-91
- ISSN: 0862-7940

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topGajewski, Herbert. "On iterative solution of nonlinear heat-conduction and diffusion problems." Aplikace matematiky 22.2 (1977): 77-91. <http://eudml.org/doc/14993>.

@article{Gajewski1977,

abstract = {The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.},

author = {Gajewski, Herbert},

journal = {Aplikace matematiky},

keywords = {diffusion problems; iterative solution; Banach fixed-point theorem; nonlinear heat-conduction; generalized Sobolev spaces of vector valued function; Diffusion Problems; Iterative Solution; Banach Fixed-Point Theorem; Nonlinear Heat-Conduction; Generalized Sobolev Spaces of Vector Valued Function},

language = {eng},

number = {2},

pages = {77-91},

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

title = {On iterative solution of nonlinear heat-conduction and diffusion problems},

url = {http://eudml.org/doc/14993},

volume = {22},

year = {1977},

}

TY - JOUR

AU - Gajewski, Herbert

TI - On iterative solution of nonlinear heat-conduction and diffusion problems

JO - Aplikace matematiky

PY - 1977

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

VL - 22

IS - 2

SP - 77

EP - 91

AB - The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.

LA - eng

KW - diffusion problems; iterative solution; Banach fixed-point theorem; nonlinear heat-conduction; generalized Sobolev spaces of vector valued function; Diffusion Problems; Iterative Solution; Banach Fixed-Point Theorem; Nonlinear Heat-Conduction; Generalized Sobolev Spaces of Vector Valued Function

UR - http://eudml.org/doc/14993

ER -

## References

top- J. R. Cannon, A. Fasano, 10.1007/BF00735697, Arch. Rat. Mech. Anal. 53 (1973), 1 - 13. (1973) Zbl0276.35061MR0348269DOI10.1007/BF00735697
- H. Gajewski, K. Gröger, Ein Iterationsverfahren für Gleichungen mit einem maximal monotonen und einem stark monotonen Lipschitzstegigen Operator, Math. Nachr. 69 (1975)307-317. (1975) MR0500342
- H. Gajewski, K. Kröger, 10.1002/mana.19750690129, Math. Nachr. 69 (1975) 319-331. (1975) MR0513156DOI10.1002/mana.19750690129
- H. Gajewski, K. Gröger, 10.1002/mana.19760730119, Math. Nachr. 73 (1976) 249-267. (1976) Zbl0352.65024MR0438697DOI10.1002/mana.19760730119
- H. Gajewski K. Grüger K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Berlin 1974. (1974)
- Y. Konishi, On the nonlinear semigroups associated with ${u}_{t}=\Delta \beta \left(u\right)$ and $\beta \left({u}_{t}\right)=\Delta u$, J. Math. Soc. Japan, 25 (1973) 622-628. (1973) MR0326517
- W. Strauss, Evolution equations non-linear in the time derivative, J. Math. Mech., 15 (1966) 49-82. (1966) Zbl0138.40001MR0190807

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