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Regularization for illposed inhomogeneous evolution problems in a Hilbert space
1.  Division of Science and Engineering, Penn State Abington, 1600 Woodland Road, Abington, PA 19001, United States 
References:
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S. Agmon and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space,, Comm. Pure Appl. Math., 16 (1963), 121. Google Scholar 
[2] 
K. A. Ames, "Comparison Results for Related Properly and Improperly Posed Problems, with Applications to Mechanics,", Ph.D. Thesis, (1980). Google Scholar 
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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 
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B. Campbell Hetrick and R. J. Hughes, Continuous dependence results for inhomogeneous illposed problems in Banach space,, J. Math. Anal. Appl., 331 (2007), 342. Google Scholar 
[5] 
N. Dunford and J. Schwartz, "Linear Operators, Part II,", John Wiley and Sons, (1957). Google Scholar 
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M. Fury and R. J. Hughes, Continuous dependence of solutions for illposed evolution problems,, Electron. J. Diff. Eqns., Conf. 19 (2010), 99. Google Scholar 
[7] 
M. A. Fury and R. J. Hughes, Regularization for a class of illposed evolution problems in Banach space,, Semigroup Forum, 85 (2012), 191. Google Scholar 
[8] 
J. A. Goldstein, "Semigroups of Linear Operators and Applications,", Oxford Univ. Press, (1985). Google Scholar 
[9] 
Y. Huang and Q. Zheng, Regularization for illposed Cauchy problems associated with generators of analytic semigroups,, J. Differential Equations, 203 (2004), 38. 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] 
T. Kato, Linear evolution equations of "hyperbolic" type,, J. Fac. Sci. Univ. Tokyo, 25 (1970), 241. Google Scholar 
[12] 
R. Lattes and J. L. Lions, "The Method of Quasireversibility, Applications to Partial Differential Equations,", Amer. Elsevier, (1969). 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] 
I. V. Mel'nikova and A. I. Filinkov, "Abstract Cauchy Problems: Three Approaches,", Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., (2001). Google Scholar 
[15] 
K. Miller, Stabilized quasireversibility and other nearlybestpossible methods for nonwellposed problems,, in, (1972), 161. Google Scholar 
[16] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", SpringerVerlag, (1983). Google Scholar 
[17] 
W. Rudin, "Real and Complex Analysis,", $3^{rd}$ edition, (1987). Google Scholar 
[18] 
R. E. Showalter, The final value problem for evolution equations,, J. Math. Anal. Appl., 47 (1974), 563. Google Scholar 
[19] 
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 
[20] 
D. D. Trong and N. H. Tuan, A nonhomogeneous backward heat problem: regularization and error estimates,, Electron. J. Diff. Eqns., 2008 (2008), 1. Google Scholar 
show all references
References:
[1] 
S. Agmon and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach space,, Comm. Pure Appl. Math., 16 (1963), 121. Google Scholar 
[2] 
K. A. Ames, "Comparison Results for Related Properly and Improperly Posed Problems, with Applications to Mechanics,", Ph.D. Thesis, (1980). Google Scholar 
[3] 
K. A. Ames and R. J. Hughes, Structural stability for illposed problems in Banach space,, Semigroup Forum, 70 (2005), 127. Google Scholar 
[4] 
B. Campbell Hetrick and R. J. Hughes, Continuous dependence results for inhomogeneous illposed problems in Banach space,, J. Math. Anal. Appl., 331 (2007), 342. Google Scholar 
[5] 
N. Dunford and J. Schwartz, "Linear Operators, Part II,", John Wiley and Sons, (1957). Google Scholar 
[6] 
M. Fury and R. J. Hughes, Continuous dependence of solutions for illposed evolution problems,, Electron. J. Diff. Eqns., Conf. 19 (2010), 99. Google Scholar 
[7] 
M. A. Fury and R. J. Hughes, Regularization for a class of illposed evolution problems in Banach space,, Semigroup Forum, 85 (2012), 191. Google Scholar 
[8] 
J. A. Goldstein, "Semigroups of Linear Operators and Applications,", Oxford Univ. Press, (1985). Google Scholar 
[9] 
Y. Huang and Q. Zheng, Regularization for illposed Cauchy problems associated with generators of analytic semigroups,, J. Differential Equations, 203 (2004), 38. 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] 
T. Kato, Linear evolution equations of "hyperbolic" type,, J. Fac. Sci. Univ. Tokyo, 25 (1970), 241. Google Scholar 
[12] 
R. Lattes and J. L. Lions, "The Method of Quasireversibility, Applications to Partial Differential Equations,", Amer. Elsevier, (1969). 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] 
I. V. Mel'nikova and A. I. Filinkov, "Abstract Cauchy Problems: Three Approaches,", Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., (2001). Google Scholar 
[15] 
K. Miller, Stabilized quasireversibility and other nearlybestpossible methods for nonwellposed problems,, in, (1972), 161. Google Scholar 
[16] 
A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations,", SpringerVerlag, (1983). Google Scholar 
[17] 
W. Rudin, "Real and Complex Analysis,", $3^{rd}$ edition, (1987). Google Scholar 
[18] 
R. E. Showalter, The final value problem for evolution equations,, J. Math. Anal. Appl., 47 (1974), 563. Google Scholar 
[19] 
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 
[20] 
D. D. Trong and N. H. Tuan, A nonhomogeneous backward heat problem: regularization and error estimates,, Electron. J. Diff. Eqns., 2008 (2008), 1. Google Scholar 
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