Convergence of Rothe's method in Hölder spaces

Norio Kikuchi; Jozef Kačur

Applications of Mathematics (2003)

  • Volume: 48, Issue: 5, page 353-365
  • ISSN: 0862-7940

Abstract

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The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.

How to cite

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Kikuchi, Norio, and Kačur, Jozef. "Convergence of Rothe's method in Hölder spaces." Applications of Mathematics 48.5 (2003): 353-365. <http://eudml.org/doc/33152>.

@article{Kikuchi2003,
abstract = {The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.},
author = {Kikuchi, Norio, Kačur, Jozef},
journal = {Applications of Mathematics},
keywords = {Rothe’s method; method of lines; convergence of Rothe’s method; method of lines},
language = {eng},
number = {5},
pages = {353-365},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence of Rothe's method in Hölder spaces},
url = {http://eudml.org/doc/33152},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Kikuchi, Norio
AU - Kačur, Jozef
TI - Convergence of Rothe's method in Hölder spaces
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 5
SP - 353
EP - 365
AB - The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.
LA - eng
KW - Rothe’s method; method of lines; convergence of Rothe’s method; method of lines
UR - http://eudml.org/doc/33152
ER -

References

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  9. L ∞ -estimates and uniform convergence of Rothe’s method for quasilinear parabolic differential equations, Methoden Verfahren Math. Phys. Vol 37, K. Kleinman et al. (eds.), Peter Lang-Verlag, 1991, pp. 187–199. (1991) MR1215747
  10. 10.4171/ZAA/706, Z. Anal. Anwendungen 15 (1996), 375–396. (1996) Zbl0851.35051MR1394434DOI10.4171/ZAA/706
  11. Function Spaces, Academia, Prague, 1977. (1977) MR0482102
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  13. The Method of Discretization in Time and Partial Differential Equations, Reidel Publishing Company, Dordrecht-Boston-London, 1982. (1982) Zbl0522.65059MR0689712

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