An extension of Rothe's method to non-cylindrical domains

Komil Kuliev; Lars-Erik Persson

Applications of Mathematics (2007)

  • Volume: 52, Issue: 5, page 365-389
  • ISSN: 0862-7940

Abstract

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In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.

How to cite

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Kuliev, Komil, and Persson, Lars-Erik. "An extension of Rothe's method to non-cylindrical domains." Applications of Mathematics 52.5 (2007): 365-389. <http://eudml.org/doc/33296>.

@article{Kuliev2007,
abstract = {In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.},
author = {Kuliev, Komil, Persson, Lars-Erik},
journal = {Applications of Mathematics},
keywords = {parabolic PDE; numerical method; time-discretization; method of lines; Rothe’s method; time-discretization; method of lines; Rothe's method; linear parabolic boundary value problems; non-cylindrical domains},
language = {eng},
number = {5},
pages = {365-389},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An extension of Rothe's method to non-cylindrical domains},
url = {http://eudml.org/doc/33296},
volume = {52},
year = {2007},
}

TY - JOUR
AU - Kuliev, Komil
AU - Persson, Lars-Erik
TI - An extension of Rothe's method to non-cylindrical domains
JO - Applications of Mathematics
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 5
SP - 365
EP - 389
AB - In this paper Rothe’s classical method is extended so that it can be used to solve some linear parabolic boundary value problems in non-cylindrical domains. The corresponding existence and uniqueness theorems are proved and some further results and generalizations are discussed and applied.
LA - eng
KW - parabolic PDE; numerical method; time-discretization; method of lines; Rothe’s method; time-discretization; method of lines; Rothe's method; linear parabolic boundary value problems; non-cylindrical domains
UR - http://eudml.org/doc/33296
ER -

References

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  1. Rothe’s method for parabolic equations on non-cylindrical domains, Advances in Algebra and Analysis 1 (2006), 1–22. (2006) MR2294649
  2. Nonlinear Differential Equations, Elsevier, Amsterdam-Oxford-New York, 1980. (1980) MR0558764
  3. Method of Rothe in Evolution Equations, Teubner, Leipzig, 1985. (1985) MR0834176
  4. Function Spaces, Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977. (1977) MR0482102
  5. The Method of Discretization in Time and Partial Differential Equations, D.  Reidel, Dordrecht-Boston-London, 1982, pp. . (1982) Zbl0522.65059MR0689712
  6. On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in space variables, Czech. Math.  J. 21 (1971), 318–339. (1971) MR0298237
  7. Variational Methods in Mathematics, Science and Engineering, D.  Reidel, Dordrecht-Boston-London, 1980. (1980) Zbl0481.49002MR0596582

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