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Volumn 23, Issue 2, 2007, Pages 823-836

Why is the Cauchy problem severely ill-posed?

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; GREEN'S FUNCTION; MATHEMATICAL OPERATORS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; SPECTRUM ANALYSIS; VARIATIONAL TECHNIQUES;

EID: 33947371334     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/2/020     Document Type: Article
Times cited : (117)

References (27)
  • 3
    • 33746272877 scopus 로고    scopus 로고
    • On Cauchy's problem: II. Completion, regularization and approximation.
    • Azaez M, Ben Belgacem F and El Fekih H 2006 On Cauchy's problem: II. Completion, regularization and approximation. Inverse Problems 22 1307-36
    • (2006) Inverse Problems , vol.22 , Issue.4 , pp. 1307-1336
    • Azaez M1    Ben Belgacem F2    El Fekih H3
  • 4
    • 28544445998 scopus 로고    scopus 로고
    • On Cauchy's problem: I. A variational Steklov-Poincaré theory
    • Ben Belgacem F and El Fekih H 2005 On Cauchy's problem: I. A variational Steklov-Poincaré theory Inverse Problems 21 1915-36
    • (2005) Inverse Problems , vol.21 , Issue.6 , pp. 1915-1936
    • Ben Belgacem F1    El Fekih H2
  • 13
    • 0000539082 scopus 로고
    • The Green function for uniformly elliptic equations
    • Grüter M and Widman K-O 1982 The Green function for uniformly elliptic equations Manuscr. Math. 37 303-42
    • (1982) Manuscr. Math. , vol.37 , Issue.3 , pp. 303-342
    • Grüter M1    Widman K-O2
  • 15
    • 0003289927 scopus 로고    scopus 로고
    • Rank-deficient and discrete ill-posed problems
    • Hansen P C 1998 Rank-deficient and discrete ill-posed problems Numerical Aspects of Linear Inversion (SIAM Monographs on Mathematical Modeling and Computation) (Philadelphia, PA: SIAM)
    • (1998) Numerical Aspects of Linear Inversion
    • Hansen P C1
  • 16
    • 0001896528 scopus 로고
    • On the characteristic values of linear integral equations
    • Hille E and Tamarkin J D 1928 On the characteristic values of linear integral equations Acta. Math. 57 1-76
    • (1928) Acta. Math. , vol.57 , Issue.1 , pp. 1-76
    • Hille E1    Tamarkin J D2
  • 18
    • 84968494628 scopus 로고
    • The existence of eigenvalues for integral operators
    • Karlin S 1964 The existence of eigenvalues for integral operators Trans. Am. Math. Soc. 113 1-17
    • (1964) Trans. Am. Math. Soc. , vol.113 , Issue.1 , pp. 1-17
    • Karlin S1
  • 20
    • 84990557216 scopus 로고
    • Determining conductivity by boundary measurements: II. Interior results
    • Kohn R V and Vogelius M S 1985 Determining conductivity by boundary measurements: II. Interior results Commun. Pure Appl. Math. 38 643-67
    • (1985) Commun. Pure Appl. Math. , vol.38 , pp. 643-667
    • Kohn R V1    Vogelius M S2
  • 22
    • 0005341464 scopus 로고
    • Eigenvalues of analytic kernels
    • Little G and Reade J B 1984 Eigenvalues of analytic kernels SIAM J. Math. Anal. 15 133-6
    • (1984) SIAM J. Math. Anal. , vol.15 , Issue.1 , pp. 133-136
    • Little G1    Reade J B2
  • 24
    • 33947388327 scopus 로고    scopus 로고
    • Rasmussen J M 2001 Compact linear operators and Krylov subspace methods Report IMM-EKS-2001-9 (Denmark: Technical University of Denmark) available at http://www2.imm.dtu.dk/documents/ftp/ep2001/ ep09_01-a.html
    • (2001) Report IMM-EKS-2001-9
    • Rasmussen J M1
  • 26
    • 33947372475 scopus 로고
    • Wahba G 1980 Ill posed problems: numerical and statistical methods for mildly, moderately and severely ill posed problems with noisy data TR 595 University of Wisconsin, Madison (Unpublished Proceedings of the Delaware Conference on Ill Posed Inverse Problems)
    • (1980) TR 595
    • Wahba G1
  • 27
    • 0001117305 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)
    • Weyl H 1912 Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung) Math. Ann. 71 441-79 (in German)
    • (1912) Math. Ann. , vol.71 , Issue.4 , pp. 441-479
    • Weyl H1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.