Continuous dependence results for inhomogeneous ill-posed problems in Banach space

Journal of Mathematical Analysis and Applications

Volumn 331, Issue 1, 2007, Pages 342-357

  Campbell Hetrick, Beth M ^a   Hughes, Rhonda J ^b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b BRYN MAWR COLLEGE   (United States)

Author keywords

Abstract Cauchy problem; Continuous dependence on modeling; Ill posed problems

Indexed keywords

EID: 33947130652     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2006.08.058     Document Type: Article

References (23)

1. Adelson L. Singular perturbation of an improperly posed Cauchy problem. SIAM J. Math. Anal. 5 (1974) 417-424
2. Agmon S., and Nirenberg L. Properties of solutions of ordinary differential equations in Banach space. Comm. Pure Appl. Math. 16 (1963) 121-151
3. Ames K.A. On the comparison of solutions of related properly and improperly posed Cauchy problems for first order operator equations. SIAM J. Math. Anal. 13 (1982) 594-606
4. Ames K.A. Some remarks on ill-posed problems for partial differential equations. Alabama J. Math. 15 (1991) 3-11
5. Ames K.A., and Cobb S.S. Continuous dependence on modeling for related Cauchy problems of a class of evolution equations. J. Math. Anal. Appl. 215 (1997) 15-31
6. Ames K.A., and Hughes R.J. Continuous dependence results for ill-posed problems. Semigroups of Operators: Theory and Applications. Second International Conference, Rio de Janeiro, Brazil, September 10-14, 2001 (2002), Optim. Softw. Publ., New York 1-8
7. Ames K.A., and Hughes R.J. Structural stability for ill-posed problems in Banach space. Semigroup Forum 70 (2005) 127-145
8. Balakrishnan A.V. Fractional powers of closed operators and the semigroups generated by them. Pacific J. Math. 10 (1960) 419-437
9. Berg C., Boyadzhiev K., and deLaubenfels R. Generation of generators of holomorphic semigroups. J. Aust. Math. Soc. 55 (1993) 246-269
10. deLaubenfels R. Powers of generators of integrated semigroups. Proc. Amer. Math. Soc. 107 (1989) 197-204
11. deLaubenfels R. Entire solutions of the abstract Cauchy problem. Semigroup Forum 42 (1991) 83-105
12. deLaubenfels R. C-Semigroups and the Cauchy problem. J. Funct. Anal. 111 (1993) 44-61
13. Fattorini H.O. The Cauchy Problem (1983), Addison-Wesley, Reading, MA
14. Goldstein J.A. Semigroups of Linear Operators and Applications (1985), Oxford Univ. Press, New York
15. Hille E. Functional Analysis and Semi-Groups. Amer. Math. Soc. Colloq. Publ. vol. 31 (1948), Amer. Math. Soc., New York
16. Lattes R., and Lions J.L. The Method of Quasi-Reversibility, Applications to Partial Differential Equations (1969), American Elsevier, New York
17. Melnikova I.V., and Filinkov A.I. Abstract Cauchy Problems: Three Approaches. Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math. vol. 120 (2001), Chapman & Hall, Boca Raton, FL
18. Miller K. Stabilized quasi-reversibility and other nearly-best-possible methods for non-well-posed problems. Symposium on Non-Well-Posed Problems and Logarithmic Convexity. Lecture Notes in Math. vol. 316 (1973), Springer, Berlin 161-176
19. Miller K. Logarithmic convexity results for holomorphic semigroups. Pacific J. Math. 58 (1975) 549-551
20. Payne L.E. Improperly Posed Problems in Partial Differential Equations. CBMS Reg. Conf. Ser. in Appl. Math. vol. 22 (1975), SIAM, Philadelphia, PA
21. Payne L.E. On stabilizing ill-posed problems against errors in geometry and modeling. Inverse and Ill-Posed Problems (1987), Academic Press, San Diego, CA 399-416
22. Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations (1983), Springer, New York
23. Showalter R.E. The final value problem for evolution equations. J. Math. Anal. Appl. 47 (1974) 563-572