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Estimates for solutions of nonautonomous semilinear illposed problems
1.  Division of Science and Engineering, Penn State Abington, 1600 Woodland Road, Abington, PA 19001 
References:
[1] 
K. A. Ames and R. J. Hughes, Structural stability for illposed problems in Banach space, Semigroup Forum, 70 (2005), 127145. Google Scholar 
[2] 
N. Boussetila and F. Rebbani, A modified quasireversibility method for a class of illposed Cauchy problems, Georgian Math J., 14 (2007), 627642. Google Scholar 
[3] 
B. Campbell Hetrick and R. J. Hughes, Continuous dependence on modeling for nonlinear illposed problems, J. Math. Anal. Appl., 349 (2009), 420435. Google Scholar 
[4] 
G. W. Clark and S. F. Oppenheimer, Quasireversibility methods for nonwellposed problems, Electron. J. Diff. Eqns., 1994 (1994), 19. Google Scholar 
[5] 
N. Dunford and J. Schwartz, Linear Operators, Part II, John Wiley and Sons, Inc., New York, 1957. Google Scholar 
[6] 
M. A. Fury, Regularization for illposed inhomogeneous evolution problems in a Hilbert space, Discrete and Continuous Dynamical Systems, 2013 (2013), Issue special, 259272. Google Scholar 
[7] 
M. A. Fury, Modified quasireversibility method for nonautonomous semilinear problems, Electron. J. Diff. Eqns., Conf. 20 (2013), 6578. Google Scholar 
[8] 
M. Fury and R. J. Hughes, Continuous dependence of solutions for illposed evolution problems, Electron. J. Diff. Eqns., Conf. 19 (2010), 99121. Google Scholar 
[9] 
Y. Huang, Modified quasireversibility method for final value problems in Banach spaces, J. Math. Anal. Appl. 340 (2008) 757769. Google Scholar 
[10] 
Y. Huang and Q. Zheng, Regularization for a class of illposed Cauchy problems, Proc. Amer. Math. Soc., 13310 (2005), 30053012. Google Scholar 
[11] 
R. Lattes and J. L. Lions, The Method of Quasireversibility, Applications to Partial Differential Equations, Amer. Elsevier, New York, 1969. Google Scholar 
[12] 
N. T. Long and A. P. N. Dinh, Approximation of a parabolic nonlinear evolution equation backwards in time, Inverse Problems, 10 (1994), 905914. Google Scholar 
[13] 
I. V. Mel'nikova, General theory of the illposed Cauchy problem, J. Inverse and Illposed Problems, 3 (1995), 149171. Google Scholar 
[14] 
K. Miller, Stabilized quasireversibility and other nearlybestpossible methods for nonwellposed problems, in Symposium on NonWellPosed Problems and Logarithmic Convexity (HeriotWatt Univ., Edinburgh, 1972), 161176, Springer Lecture Notes in Mathematics, Volume 316, Springer, Berlin, 1973. Google Scholar 
[15] 
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, SpringerVerlag, New York, 1983. Google Scholar 
[16] 
R. E. Showalter, The final value problem for evolution equations, J. Math. Anal. Appl., 47 (1974), 563572. Google Scholar 
[17] 
D. D. Trong and N. H. Tuan, Regularization and error estimates for nonhomogeneous backward heat problems, Electron. J. Diff. Eqns., 2006 (2006), 110. Google Scholar 
[18] 
D. D. Trong and N. H. Tuan, Stabilized quasireversibility method for a class of nonlinear illposed problems, Electron. J. Diff. Eqns., 2008 (2008), 112. Google Scholar 
[19] 
N. H. Tuan and D. D. Trong, On a backward parabolic problem with local Lipschitz source, J. Math. Anal. Appl. 414 (2014), 678692. Google Scholar 
show all references
References:
[1] 
K. A. Ames and R. J. Hughes, Structural stability for illposed problems in Banach space, Semigroup Forum, 70 (2005), 127145. Google Scholar 
[2] 
N. Boussetila and F. Rebbani, A modified quasireversibility method for a class of illposed Cauchy problems, Georgian Math J., 14 (2007), 627642. Google Scholar 
[3] 
B. Campbell Hetrick and R. J. Hughes, Continuous dependence on modeling for nonlinear illposed problems, J. Math. Anal. Appl., 349 (2009), 420435. Google Scholar 
[4] 
G. W. Clark and S. F. Oppenheimer, Quasireversibility methods for nonwellposed problems, Electron. J. Diff. Eqns., 1994 (1994), 19. Google Scholar 
[5] 
N. Dunford and J. Schwartz, Linear Operators, Part II, John Wiley and Sons, Inc., New York, 1957. Google Scholar 
[6] 
M. A. Fury, Regularization for illposed inhomogeneous evolution problems in a Hilbert space, Discrete and Continuous Dynamical Systems, 2013 (2013), Issue special, 259272. Google Scholar 
[7] 
M. A. Fury, Modified quasireversibility method for nonautonomous semilinear problems, Electron. J. Diff. Eqns., Conf. 20 (2013), 6578. Google Scholar 
[8] 
M. Fury and R. J. Hughes, Continuous dependence of solutions for illposed evolution problems, Electron. J. Diff. Eqns., Conf. 19 (2010), 99121. Google Scholar 
[9] 
Y. Huang, Modified quasireversibility method for final value problems in Banach spaces, J. Math. Anal. Appl. 340 (2008) 757769. Google Scholar 
[10] 
Y. Huang and Q. Zheng, Regularization for a class of illposed Cauchy problems, Proc. Amer. Math. Soc., 13310 (2005), 30053012. Google Scholar 
[11] 
R. Lattes and J. L. Lions, The Method of Quasireversibility, Applications to Partial Differential Equations, Amer. Elsevier, New York, 1969. Google Scholar 
[12] 
N. T. Long and A. P. N. Dinh, Approximation of a parabolic nonlinear evolution equation backwards in time, Inverse Problems, 10 (1994), 905914. Google Scholar 
[13] 
I. V. Mel'nikova, General theory of the illposed Cauchy problem, J. Inverse and Illposed Problems, 3 (1995), 149171. Google Scholar 
[14] 
K. Miller, Stabilized quasireversibility and other nearlybestpossible methods for nonwellposed problems, in Symposium on NonWellPosed Problems and Logarithmic Convexity (HeriotWatt Univ., Edinburgh, 1972), 161176, Springer Lecture Notes in Mathematics, Volume 316, Springer, Berlin, 1973. Google Scholar 
[15] 
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, SpringerVerlag, New York, 1983. Google Scholar 
[16] 
R. E. Showalter, The final value problem for evolution equations, J. Math. Anal. Appl., 47 (1974), 563572. Google Scholar 
[17] 
D. D. Trong and N. H. Tuan, Regularization and error estimates for nonhomogeneous backward heat problems, Electron. J. Diff. Eqns., 2006 (2006), 110. Google Scholar 
[18] 
D. D. Trong and N. H. Tuan, Stabilized quasireversibility method for a class of nonlinear illposed problems, Electron. J. Diff. Eqns., 2008 (2008), 112. Google Scholar 
[19] 
N. H. Tuan and D. D. Trong, On a backward parabolic problem with local Lipschitz source, J. Math. Anal. Appl. 414 (2014), 678692. Google Scholar 
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