Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

Author(s): Nguyen Minh Chuong; Bui Kien Cuong
Journal: Proc. Amer. Math. Soc. 132 (2004), 3589-3597.
MSC (2000): Primary 35A40, 65D05, 65M06, 65M12, 65M15
Posted: July 22, 2004
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.


References:

1.
M.V. Altaiski, p-adic wavelet decomposition vs Fourier analysis on spheres, Indian J. pure appl. Math. 1997, 28(2):197-205. MR 98b:42056

2.
G. Beyklin, R. Coifman and V. Rocklin, Fast wavelet transforms and Numerical Algorithms I, Communications on Pure and Applied Mathematics, vol. XLIV (1991) 141-183. MR 92c:65061

3.
Nguyen Minh Chuong, Nguyen Minh Tri and Le Quang Trung, Theory of partial differential equations, Sci. and Techn. Publishing House, Hanoi, 1995.MR 99c:35001

4.
Nguyen Minh Chuong (Chief Author), Nguyen Van Khai, Khuat Van Ninh, Nguyen Van Tuan, and Nguyen Tuong, Numerical Analysis, Education Publishing House, Hanoi, 2001.

5.
Nguyen Minh Chuong, Parabolic pseudodifferential operators of variable order, Dokl. Akad. Nauk SSSR 258(1981), No 6, 1308-1312. MR 83b:35077

6.
Nguyen Minh Chuong, Parabolic pseudodifferential operators of variable order in Sobolev spaces with weighted norms, Dokl. Akad. Nauk SSSR 264(1982), No 2, 299-302. MR 83m:35151

7.
Nguyen Minh Chuong, Degenerate parabolic pseudodifferential operators of variable order, Dokl. Akad. Nauk SSSR 268(1983), No 5, 1055-1058, MR 85g:35068

8.
Nguyen Minh Chuong and Bui Kien Cuong, Galerkin-wavelet approximation for a class of partial integro-differential equations, Fractional Calculus and Applied Analysis, 4(2001), No 2, 143-152. MR 2002c:65246

9.
Nguyen Minh Chuong and Ta Ngoc Tri, The integral wavelet transform in $L_p({\mathbb{R} })$, $ 1\le p\le \infty $, Fractional Calculus and Applied Analysis, 3(2000), No 2, 133-140. MR 2001k:42035

10.
Nguyen Minh Chuong and Bui Kien Cuong, The convergence estimates for Galerkin-wavelet method for initial pseudodifferential periodic problems, International J. of Math. Sciences, Volume 2003, No 14, 857-867. MR 2004b:35350

11.
Nguyen Minh Chuong (Chief Author), Ha Tien Ngoan, Nguyen Minh Tri, and Le Quang Trung, Partial Differential Equations, Second Edition, Education Publishing House, Hanoi, 2000. MR 2001i:35001

12.
Nguyen Minh Chuong and Nguyen Van Co, The multidimensional p-adic Green Function, Proc. AMS, 127(1999), No 3, 385, 694. MR 99i:11109
13.
Stephan Dahlke and Ilona Weindrich, Wavelet bases Adapted to Pseudodifferential Operators, Applied and Computational Harmonic Analysis, 1(1994), 267-283. MR 96a:35226

14.
W. Dahmen, S. Prössdorf, R. Schneider, Wavelet approximation methods for pseudodiffirential equation I: Stability and convergence, Math. Zeist. Springer-Verlag, 215(1994), 583-620. MR 95g:65148

15.
David L. Donoho, Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data, Proc. Sympos. Appl. Math. 47, AMS, Providence, RI, (1993). MR 95k:62099

16.
Yu. V. Egorov, Nguyen Minh Chuong, On some semilinear boundary value problems for singular integro-differential equations, Russian Math. Surveys, 53(1998), No 6, 1348-1349. MR 2000j:35040

17.
Peter R. Massopust, Fractal functions, fractal surfaces, and wavelets, Academic Press, San Diego, New York, Boston, London, Sydney, Tokyo, Toronto, 1994. MR 96b:28007

18.
Y. Meyer, Ondelettes et Opérators, I, II, Hermann, Paris, 1990, MR 93i:42002; MR 93i:42003

19.
L. Hörmander, The analysis of linear partial operator, III, IV, Springer-Verlag, Berlin Heidelberg New York Tokyo, 1985. MR 88m:35001; MR 89k:35002

20.
V. Strela and G. Strang, Finite element multiwavelets, Approximation Theory and Applications, Maratea, 1994, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 454. MR 96c:42072

21.
M. E. Taylor, Noncommutative Microlocal Analysis, Memoirs of the AMS, part I, Vol. 52, No. 313, AMS Providence, RI, 1984. MR 86f:58156

22.
F. Trèves, Introduction to pseudodifferential and Fourier Integral Operators, I, II, Plenum Press. New York and London, 1982, MR 85d:58077; MR 85d:35110


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35A40, 65D05, 65M06, 65M12, 65M15

Retrieve articles in all Journals with MSC (2000): 35A40, 65D05, 65M06, 65M12, 65M15


Additional Information:

Nguyen Minh Chuong
Affiliation: Hanoi Institute of Mathematics, P.O. Box 631 Bo Ho, 10 000 Hanoi, Vietnam
Email: nmchuong@math.ac.vn

Bui Kien Cuong
Affiliation: Hanoi Institute of Mathematics, P.O. Box 631 Bo Ho, 10 000 Hanoi, Vietnam

DOI: 10.1090/S0002-9939-04-07434-9
PII: S 0002-9939(04)07434-9
Keywords: Convergence estimates, weak Galerkin-wavelet solution, Cauchy problem, periodic pseudodifferential equations.
Received by editor(s): November 15, 2001
Received by editor(s) in revised form: June 20, 2003
Posted: July 22, 2004
Communicated by: David R. Larson
Copyright of article: Copyright 2004, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google