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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:
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K. A. Ames and R. J. Hughes, Structural stability for illposed problems in Banach space,, Semigroup Forum, 70 (2005), 127. Google Scholar 
[2] 
N. Boussetila and F. Rebbani, A modified quasireversibility method for a class of illposed Cauchy problems,, Georgian Math J., 14 (2007), 627. Google Scholar 
[3] 
B. Campbell Hetrick and R. J. Hughes, Continuous dependence on modeling for nonlinear illposed problems,, J. Math. Anal. Appl., 349 (2009), 420. Google Scholar 
[4] 
G. W. Clark and S. F. Oppenheimer, Quasireversibility methods for nonwellposed problems,, Electron. J. Diff. Eqns., 1994 (1994), 1. Google Scholar 
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N. Dunford and J. Schwartz, Linear Operators, Part II,, John Wiley and Sons, (1957). Google Scholar 
[6] 
M. A. Fury, Regularization for illposed inhomogeneous evolution problems in a Hilbert space,, Discrete and Continuous Dynamical Systems, 2013 (2013), 259. Google Scholar 
[7] 
M. A. Fury, Modified quasireversibility method for nonautonomous semilinear problems,, Electron. J. Diff. Eqns., Conf. 20 (2013), 65. Google Scholar 
[8] 
M. Fury and R. J. Hughes, Continuous dependence of solutions for illposed evolution problems,, Electron. J. Diff. Eqns., Conf. 19 (2010), 99. Google Scholar 
[9] 
Y. Huang, Modified quasireversibility method for final value problems in Banach spaces,, J. Math. Anal. Appl. 340 (2008) 757769., 340 (2008), 757. Google Scholar 
[10] 
Y. Huang and Q. Zheng, Regularization for a class of illposed Cauchy problems,, Proc. Amer. Math. Soc., 13310 (2005), 133. Google Scholar 
[11] 
R. Lattes and J. L. Lions, The Method of Quasireversibility, Applications to Partial Differential Equations,, Amer. Elsevier, (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), 905. Google Scholar 
[13] 
I. V. Mel'nikova, General theory of the illposed Cauchy problem,, J. Inverse and Illposed Problems, 3 (1995), 149. Google Scholar 
[14] 
K. Miller, Stabilized quasireversibility and other nearlybestpossible methods for nonwellposed problems,, in Symposium on NonWellPosed Problems and Logarithmic Convexity (HeriotWatt Univ., (1972), 161. Google Scholar 
[15] 
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, SpringerVerlag, (1983). Google Scholar 
[16] 
R. E. Showalter, The final value problem for evolution equations,, J. Math. Anal. Appl., 47 (1974), 563. 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), 1. 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), 1. 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), 414 (2014), 678. 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), 127. Google Scholar 
[2] 
N. Boussetila and F. Rebbani, A modified quasireversibility method for a class of illposed Cauchy problems,, Georgian Math J., 14 (2007), 627. Google Scholar 
[3] 
B. Campbell Hetrick and R. J. Hughes, Continuous dependence on modeling for nonlinear illposed problems,, J. Math. Anal. Appl., 349 (2009), 420. Google Scholar 
[4] 
G. W. Clark and S. F. Oppenheimer, Quasireversibility methods for nonwellposed problems,, Electron. J. Diff. Eqns., 1994 (1994), 1. Google Scholar 
[5] 
N. Dunford and J. Schwartz, Linear Operators, Part II,, John Wiley and Sons, (1957). Google Scholar 
[6] 
M. A. Fury, Regularization for illposed inhomogeneous evolution problems in a Hilbert space,, Discrete and Continuous Dynamical Systems, 2013 (2013), 259. Google Scholar 
[7] 
M. A. Fury, Modified quasireversibility method for nonautonomous semilinear problems,, Electron. J. Diff. Eqns., Conf. 20 (2013), 65. Google Scholar 
[8] 
M. Fury and R. J. Hughes, Continuous dependence of solutions for illposed evolution problems,, Electron. J. Diff. Eqns., Conf. 19 (2010), 99. Google Scholar 
[9] 
Y. Huang, Modified quasireversibility method for final value problems in Banach spaces,, J. Math. Anal. Appl. 340 (2008) 757769., 340 (2008), 757. Google Scholar 
[10] 
Y. Huang and Q. Zheng, Regularization for a class of illposed Cauchy problems,, Proc. Amer. Math. Soc., 13310 (2005), 133. Google Scholar 
[11] 
R. Lattes and J. L. Lions, The Method of Quasireversibility, Applications to Partial Differential Equations,, Amer. Elsevier, (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), 905. Google Scholar 
[13] 
I. V. Mel'nikova, General theory of the illposed Cauchy problem,, J. Inverse and Illposed Problems, 3 (1995), 149. Google Scholar 
[14] 
K. Miller, Stabilized quasireversibility and other nearlybestpossible methods for nonwellposed problems,, in Symposium on NonWellPosed Problems and Logarithmic Convexity (HeriotWatt Univ., (1972), 161. Google Scholar 
[15] 
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations,, SpringerVerlag, (1983). Google Scholar 
[16] 
R. E. Showalter, The final value problem for evolution equations,, J. Math. Anal. Appl., 47 (1974), 563. 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), 1. 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), 1. 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), 414 (2014), 678. Google Scholar 
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