Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
parabolic PDE; numerical method; time-discretization; method of lines; Rothe’s method
parabolic PDE; numerical method; time-discretization; method of lines; Rothe’s method
Summary:
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.
References:
[1] J. Dasht, J. Engström, A. Kufner, and L.-E. Persson: Rothe’s method for parabolic equations on non-cylindrical domains. Advances in Algebra and Analysis 1 (2006), 1–22. MR 2294649
[2] S. Fučík, A. Kufner: Nonlinear Differential Equations. Elsevier, Amsterdam-Oxford-New York, 1980. MR 0558764
[3] J. Kačur: Method of Rothe in Evolution Equations. Teubner, Leipzig, 1985. MR 0834176
[4] A. Kufner, O. John, and S. Fučík: Function Spaces. Academia, Publishing House of the Czechoslovak Academy of Sciences, Prague, 1977. MR 0482102
[5] K. Rektorys: The Method of Discretization in Time and Partial Differential Equations. D. Reidel, Dordrecht-Boston-London, 1982, pp. . MR 0689712 | Zbl 0522.65059
[6] K. Rektorys: 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. MR 0298237
[7] K. Rektorys: Variational Methods in Mathematics, Science and Engineering. D. Reidel, Dordrecht-Boston-London, 1980. MR 0596582 | Zbl 0481.49002
Search
Partner of
