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Volumn 2008, Issue , 2008, Pages 1-12

Stabilized quasi-reversibility method for a class of nonlinear ill-posed problems

Author keywords

Ill posed problem; Nonlinear parabolic equation; Quasi reversibility methods; Stabilized quasi reversibility methods

Indexed keywords


EID: 45149119185     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (16)

References (33)
  • 1
    • 22444452339 scopus 로고    scopus 로고
    • The quasi-reversibility method for the problem of the control of an initial condition for the heat equation with an integral boundary condition
    • S. M. Alekseeva, N. I. Yurchuk; The quasi-reversibility method for the problem of the control of an initial condition for the heat equation with an integral boundary condition, Differential Equations 34, no. 4,493-500, 1998.
    • (1998) Differential Equations , vol.34 , Issue.4 , pp. 493-500
    • Alekseeva, S.M.1    Yurchuk, N.I.2
  • 2
    • 1942417404 scopus 로고    scopus 로고
    • Continuous dependence on modeling for some well-posed perturbations of the backward heat equation
    • K. A. Ames, L. E. Payne; Continuous dependence on modeling for some well-posed perturbations of the backward heat equation, J. Inequal. Appl., Vol. 3 (1999), 51-64.
    • (1999) J. Inequal. Appl , vol.3 , pp. 51-64
    • Ames, K.A.1    Payne, L.E.2
  • 3
    • 24044524460 scopus 로고    scopus 로고
    • Structural Stability for Ill-Posed Problems in Banach Space
    • 1
    • K. A. Ames, R. J. Hughes; Structural Stability for Ill-Posed Problems in Banach Space, Semigroup Forum, Vol. 70 (2005), N0 1, 127-145.
    • (2005) Semigroup Forum , vol.70 , Issue.N0 , pp. 127-145
    • Ames, K.A.1    Hughes, R.J.2
  • 5
    • 0007447039 scopus 로고
    • Quasireversibility methods for non-well posed problems
    • G. W. Clark, S. F. Oppenheimer; Quasireversibility methods for non-well posed problems, Elect. J. Diff. Eqns., 1994 (1994) no. 8, 1-9.
    • (1994) Elect. J. Diff. Eqns , vol.1994 , Issue.8 , pp. 1-9
    • Clark, G.W.1    Oppenheimer, S.F.2
  • 6
    • 0345854822 scopus 로고    scopus 로고
    • Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition
    • M. Denche, K. Bessila; Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition, Math. Probl. Eng. 7, no. 2, 129-145, 2001.
    • (2001) Math. Probl. Eng , vol.7 , Issue.2 , pp. 129-145
    • Denche, M.1    Bessila, K.2
  • 7
    • 10344263455 scopus 로고    scopus 로고
    • A modified quasi-boundary value method for ill-posed problems
    • M. Denche, K. Bessila; A modified quasi-boundary value method for ill-posed problems, J. Math. Anal. Appl, Vol. 301, 2005, pp. 419-426.
    • (2005) J. Math. Anal. Appl , vol.301 , pp. 419-426
    • Denche, M.1    Bessila, K.2
  • 8
    • 0007415654 scopus 로고
    • The approximation of certain parabolic equations backward in time by Sobolev equations
    • R. E. Ewing; The approximation of certain parabolic equations backward in time by Sobolev equations, SIAM J. Math. Anal., Vol. 6 (1975), No. 2, 283-294.
    • (1975) SIAM J. Math. Anal , vol.6 , Issue.2 , pp. 283-294
    • Ewing, R.E.1
  • 9
    • 4544318973 scopus 로고
    • Zur regularisierung einer klass nichtkorrekter probleme bei evolutiongleichungen
    • H. Gajewski, K. Zaccharias; Zur regularisierung einer klass nichtkorrekter probleme bei evolutiongleichungen, J. Math. Anal. Appl., Vol. 38 (1972), 784-789.
    • (1972) J. Math. Anal. Appl , vol.38 , pp. 784-789
    • Gajewski, H.1    Zaccharias, K.2
  • 10
    • 0035311244 scopus 로고    scopus 로고
    • A numerical method for backward parabolic problems with non-selfadjoint elliptic operator
    • A. Hassanov, J.L. Mueller; A numerical method for backward parabolic problems with non-selfadjoint elliptic operator, Applied Numerical Mathematics, 37 (2001), 55-78.
    • (2001) Applied Numerical Mathematics , vol.37 , pp. 55-78
    • Hassanov, A.1    Mueller, J.L.2
  • 11
    • 33947130652 scopus 로고    scopus 로고
    • Continuous dependence results for inhomogeneous ill-posed problems in Banach space
    • 1 July
    • Beth M. Campbell Hetrick and Rhonda J. Hughes Continuous dependence results for inhomogeneous ill-posed problems in Banach space, Journal of Mathematical Analysis and Applications, Volume 331, Issue 1, 1 July 2007, Pages 342-357
    • (2007) Journal of Mathematical Analysis and Applications , vol.331 , Issue.1 , pp. 342-357
    • Campbell Hetrick, B.M.1    Hughes, R.J.2
  • 12
    • 3042689022 scopus 로고    scopus 로고
    • Regularization for ill-posed Cauchy problems associated with generators of analytic semigroups
    • Y. Huang, Q. Zhneg; Regularization for ill-posed Cauchy problems associated with generators of analytic semigroups, J. Differential Equations, Vol. 203 (2004), No. 1, 38-54.
    • (2004) J. Differential Equations , vol.203 , Issue.1 , pp. 38-54
    • Huang, Y.1    Zhneg, Q.2
  • 13
    • 38049053558 scopus 로고    scopus 로고
    • Modified quasi-reversibility method for final value problems in Banach spaces
    • Y. Huang; Modified quasi-reversibility method for final value problems in Banach spaces , J. Math. Anal. Appl. 340 (2008) 757769.
    • (2008) J. Math. Anal. Appl , vol.340 , pp. 757769
    • Huang, Y.1
  • 15
    • 84980073634 scopus 로고
    • Continuous dependence on data for solutions of partial differential equations with a prescribed bound
    • F. John; Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math, 13 (1960), 551-585.
    • (1960) Comm. Pure Appl. Math , vol.13 , pp. 551-585
    • John, F.1
  • 16
    • 0000710664 scopus 로고
    • On the iterative method for solving ill-posed boundary value problems that preserve differential equations
    • V. A. Kozlov, V. G. Maz'ya; On the iterative method for solving ill-posed boundary value problems that preserve differential equations, Leningrad Math. J., 1 (1990), No. 5, 1207-1228.
    • (1990) Leningrad Math. J , vol.1 , Issue.5 , pp. 1207-1228
    • Kozlov, V.A.1    Maz'ya, V.G.2
  • 18
    • 10444242627 scopus 로고
    • Ding; Approximation of a parabolic non-linear evolution equation backwards in time
    • N. T. Long, A. P. Ngoc. Ding; Approximation of a parabolic non-linear evolution equation backwards in time, Inv. Problems, 10 (1994), 905-914.
    • (1994) Inv. Problems , vol.10 , pp. 905-914
    • Long, N.T.1    Ngoc, A.P.2
  • 19
    • 45149122404 scopus 로고    scopus 로고
    • I. V. Mel'nikova, Q. Zheng and J. Zheng; Regularization of weakly ill-posed Cauchy problem, J. Inv. Ill-posed Problems, 10 (2002), No. 5, 385-393.
    • I. V. Mel'nikova, Q. Zheng and J. Zheng; Regularization of weakly ill-posed Cauchy problem, J. Inv. Ill-posed Problems, Vol. 10 (2002), No. 5, 385-393.
  • 20
    • 33751516621 scopus 로고
    • C-semigroups and regularization of an ill-posed Cauchy problem
    • I. V. Mel'nikova, S. V. Bochkareva; C-semigroups and regularization of an ill-posed Cauchy problem, Dok. Akad. Nauk., 329 (1993), 270-273.
    • (1993) Dok. Akad. Nauk , vol.329 , pp. 270-273
    • Mel'nikova, I.V.1    Bochkareva, S.V.2
  • 22
    • 0040225041 scopus 로고
    • Stabilized quasi-reversibility and other nearly-best-possible methods for non-well posed problems
    • Symposium on Non-Well Posed Problems and Logarithmic Convexity, Springer-Verlag, Berlin
    • K. Miller; 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 Mathematics, 316 (1973), Springer-Verlag, Berlin , 161-176.
    • (1973) Lecture Notes in Mathematics , vol.316 , pp. 161-176
    • Miller, K.1
  • 23
    • 0039633099 scopus 로고
    • Some general remarks on improperly posed problems for partial differential equations
    • Symposium on Non-Well Posed Problems and Logarithmic Convexity, Springer-Verlag, Berlin
    • L. E. Payne; Some general remarks on improperly posed problems for partial differential equations, Symposium on Non-Well Posed Problems and Logarithmic Convexity, Lecture Notes in Mathematics, 316 (1973), Springer-Verlag, Berlin, 1-30.
    • (1973) Lecture Notes in Mathematics , vol.316 , pp. 1-30
    • Payne, L.E.1
  • 26
    • 33751542352 scopus 로고
    • Estimates for the rate of convergence in the solution of ill-posed problems for evolution equations
    • S. Piskarev; Estimates for the rate of convergence in the solution of ill-posed problems for evolution equations, Izv. Akad. Nauk SSSR Ser. Mat., 51 (1987), 676-687.
    • (1987) Izv. Akad. Nauk SSSR Ser. Mat , vol.51 , pp. 676-687
    • Piskarev, S.1
  • 27
    • 85064030485 scopus 로고    scopus 로고
    • P. H. Quan, D. D. Trong, D. D., A nonlinearly backward heat problem: uniqueness, regularization and error estimate, Applicable Analysis, 85, Nos. 6-7, June-July 2006, pp. 641-657.
    • P. H. Quan, D. D. Trong, D. D., A nonlinearly backward heat problem: uniqueness, regularization and error estimate, Applicable Analysis, Vol. 85, Nos. 6-7, June-July 2006, pp. 641-657.
  • 29
    • 0039633096 scopus 로고
    • The final value problem for evolution equations
    • R. E. Showalter; The final value problem for evolution equations, J. Math. Anal. Appl, 47 (1974), 563-572.
    • (1974) J. Math. Anal. Appl , vol.47 , pp. 563-572
    • Showalter, R.E.1
  • 31
    • 45149084048 scopus 로고    scopus 로고
    • R. E. Showalter, Quasi-reversibility of first and second order parabolic evolution equations, Improperly posed boundary value problems (Conf., Univ. New Mexico, Albuquerque, N. M., 1974), pp. 76-84. Res. Notes in Math., no. 1, Pitman, London, 1975.
    • R. E. Showalter, Quasi-reversibility of first and second order parabolic evolution equations, Improperly posed boundary value problems (Conf., Univ. New Mexico, Albuquerque, N. M., 1974), pp. 76-84. Res. Notes in Math., no. 1, Pitman, London, 1975.
  • 32
    • 30544431837 scopus 로고    scopus 로고
    • Regularization and error estimates for nonhomogeneous backward heat problems
    • D. D. Trong, N. H. Tuan; Regularization and error estimates for nonhomogeneous backward heat problems, Electron. J. Diff. Eqns., Vol. 2006, No. 04, 2006, pp. 1-10.
    • (2006) Electron. J. Diff. Eqns , vol.2006 , Issue.4 , pp. 1-10
    • Trong, D.D.1    Tuan, N.H.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.