
Previous Article
Existence of nontrivial solutions to systems of multipoint boundary value problems
 PROC Home
 This Issue

Next Article
Characterization of the spectral density function for a onesided tridiagonal Jacobi matrix operator
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:
[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 
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 
[1] 
Paola Favati, Grazia Lotti, Ornella Menchi, Francesco Romani. An innerouter regularizing method for illposed problems. Inverse Problems & Imaging, 2014, 8 (2) : 409420. doi: 10.3934/ipi.2014.8.409 
[2] 
Markus Haltmeier, Richard Kowar, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear illposed equations II: Applications. Inverse Problems & Imaging, 2007, 1 (3) : 507523. doi: 10.3934/ipi.2007.1.507 
[3] 
Markus Haltmeier, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear illposed equations I: convergence analysis. Inverse Problems & Imaging, 2007, 1 (2) : 289298. doi: 10.3934/ipi.2007.1.289 
[4] 
Eliane Bécache, Laurent Bourgeois, Lucas Franceschini, Jérémi Dardé. Application of mixed formulations of quasireversibility to solve illposed problems for heat and wave equations: The 1D case. Inverse Problems & Imaging, 2015, 9 (4) : 9711002. doi: 10.3934/ipi.2015.9.971 
[5] 
Stefan Kindermann. Convergence of the gradient method for illposed problems. Inverse Problems & Imaging, 2017, 11 (4) : 703720. doi: 10.3934/ipi.2017033 
[6] 
Sergiy Zhuk. Inverse problems for linear illposed differentialalgebraic equations with uncertain parameters. Conference Publications, 2011, 2011 (Special) : 14671476. doi: 10.3934/proc.2011.2011.1467 
[7] 
Matthew A. Fury. Estimates for solutions of nonautonomous semilinear illposed problems. Conference Publications, 2015, 2015 (special) : 479488. doi: 10.3934/proc.2015.0479 
[8] 
Misha Perepelitsa. An illposed problem for the NavierStokes equations for compressible flows. Discrete & Continuous Dynamical Systems  A, 2010, 26 (2) : 609623. doi: 10.3934/dcds.2010.26.609 
[9] 
Felix Lucka, Katharina Proksch, Christoph Brune, Nicolai Bissantz, Martin Burger, Holger Dette, Frank Wübbeling. Risk estimators for choosing regularization parameters in illposed problems  properties and limitations. Inverse Problems & Imaging, 2018, 12 (5) : 11211155. doi: 10.3934/ipi.2018047 
[10] 
Olha P. Kupenko, Rosanna Manzo. On optimal controls in coefficients for illposed nonLinear elliptic Dirichlet boundary value problems. Discrete & Continuous Dynamical Systems  B, 2018, 23 (4) : 13631393. doi: 10.3934/dcdsb.2018155 
[11] 
Guozhi Dong, Bert Jüttler, Otmar Scherzer, Thomas Takacs. Convergence of Tikhonov regularization for solving illposed operator equations with solutions defined on surfaces. Inverse Problems & Imaging, 2017, 11 (2) : 221246. doi: 10.3934/ipi.2017011 
[12] 
Johann Baumeister, Barbara Kaltenbacher, Antonio Leitão. On LevenbergMarquardtKaczmarz iterative methods for solving systems of nonlinear illposed equations. Inverse Problems & Imaging, 2010, 4 (3) : 335350. doi: 10.3934/ipi.2010.4.335 
[13] 
Adriano De Cezaro, Johann Baumeister, Antonio Leitão. Modified iterated Tikhonov methods for solving systems of nonlinear illposed equations. Inverse Problems & Imaging, 2011, 5 (1) : 117. doi: 10.3934/ipi.2011.5.1 
[14] 
Lianwang Deng. Local integral manifolds for nonautonomous and illposed equations with sectorially dichotomous operator. Communications on Pure & Applied Analysis, 2020, 19 (1) : 145174. doi: 10.3934/cpaa.2020009 
[15] 
Peter I. Kogut, Olha P. Kupenko. On optimal control problem for an illposed strongly nonlinear elliptic equation with $p$Laplace operator and $L^1$type of nonlinearity. Discrete & Continuous Dynamical Systems  B, 2019, 24 (3) : 12731295. doi: 10.3934/dcdsb.2019016 
[16] 
Youri V. Egorov, Evariste SanchezPalencia. Remarks on certain singular perturbations with illposed limit in shell theory and elasticity. Discrete & Continuous Dynamical Systems  A, 2011, 31 (4) : 12931305. doi: 10.3934/dcds.2011.31.1293 
[17] 
Alfredo Lorenzi, Luca Lorenzi. A strongly illposed integrodifferential singular parabolic problem in the unit cube of $\mathbb{R}^n$. Evolution Equations & Control Theory, 2014, 3 (3) : 499524. doi: 10.3934/eect.2014.3.499 
[18] 
Faker Ben Belgacem. Uniqueness for an illposed reactiondispersion model. Application to organic pollution in streamwaters. Inverse Problems & Imaging, 2012, 6 (2) : 163181. doi: 10.3934/ipi.2012.6.163 
[19] 
Noboru Okazawa, Kentarou Yoshii. Linear evolution equations with strongly measurable families and application to the Dirac equation. Discrete & Continuous Dynamical Systems  S, 2011, 4 (3) : 723744. doi: 10.3934/dcdss.2011.4.723 
[20] 
Sebastián Ferrer, Martin Lara. Families of canonical transformations by HamiltonJacobiPoincaré equation. Application to rotational and orbital motion. Journal of Geometric Mechanics, 2010, 2 (3) : 223241. doi: 10.3934/jgm.2010.2.223 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]