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A computational method for an inverse problem in a parabolic system
1.  Dept. of Mechanical Engineering, University of Colorado Denver, Denver, CO 80217, United States 
[1] 
Alfredo Lorenzi, Luca Lorenzi. A strongly illposed integrodifferential singular parabolic problem in the unit cube of $\mathbb{R}^n$. Evolution Equations and Control Theory, 2014, 3 (3) : 499524. doi: 10.3934/eect.2014.3.499 
[2] 
Misha Perepelitsa. An illposed problem for the NavierStokes equations for compressible flows. Discrete and Continuous Dynamical Systems, 2010, 26 (2) : 609623. doi: 10.3934/dcds.2010.26.609 
[3] 
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 and Continuous Dynamical Systems  B, 2019, 24 (3) : 12731295. doi: 10.3934/dcdsb.2019016 
[4] 
Ye Zhang, Bernd Hofmann. Two new nonnegativity preserving iterative regularization methods for illposed inverse problems. Inverse Problems and Imaging, 2021, 15 (2) : 229256. doi: 10.3934/ipi.2020062 
[5] 
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 
[6] 
Stefan Kindermann. Convergence of the gradient method for illposed problems. Inverse Problems and Imaging, 2017, 11 (4) : 703720. doi: 10.3934/ipi.2017033 
[7] 
Markus Haltmeier, Richard Kowar, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear illposed equations II: Applications. Inverse Problems and Imaging, 2007, 1 (3) : 507523. doi: 10.3934/ipi.2007.1.507 
[8] 
Matthew A. Fury. Estimates for solutions of nonautonomous semilinear illposed problems. Conference Publications, 2015, 2015 (special) : 479488. doi: 10.3934/proc.2015.0479 
[9] 
Paola Favati, Grazia Lotti, Ornella Menchi, Francesco Romani. An innerouter regularizing method for illposed problems. Inverse Problems and Imaging, 2014, 8 (2) : 409420. doi: 10.3934/ipi.2014.8.409 
[10] 
Matthew A. Fury. Regularization for illposed inhomogeneous evolution problems in a Hilbert space. Conference Publications, 2013, 2013 (special) : 259272. doi: 10.3934/proc.2013.2013.259 
[11] 
Zonghao Li, Caibin Zeng. Center manifolds for illposed stochastic evolution equations. Discrete and Continuous Dynamical Systems  B, 2022, 27 (5) : 24832499. doi: 10.3934/dcdsb.2021142 
[12] 
Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$System at a Junction. Networks and Heterogeneous Media, 2006, 1 (3) : 495511. doi: 10.3934/nhm.2006.1.495 
[13] 
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 and Imaging, 2018, 12 (5) : 11211155. doi: 10.3934/ipi.2018047 
[14] 
Guozhi Dong, Bert Jüttler, Otmar Scherzer, Thomas Takacs. Convergence of Tikhonov regularization for solving illposed operator equations with solutions defined on surfaces. Inverse Problems and Imaging, 2017, 11 (2) : 221246. doi: 10.3934/ipi.2017011 
[15] 
Lianwang Deng. Local integral manifolds for nonautonomous and illposed equations with sectorially dichotomous operator. Communications on Pure and Applied Analysis, 2020, 19 (1) : 145174. doi: 10.3934/cpaa.2020009 
[16] 
Youri V. Egorov, Evariste SanchezPalencia. Remarks on certain singular perturbations with illposed limit in shell theory and elasticity. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 12931305. doi: 10.3934/dcds.2011.31.1293 
[17] 
Johann Baumeister, Barbara Kaltenbacher, Antonio Leitão. On LevenbergMarquardtKaczmarz iterative methods for solving systems of nonlinear illposed equations. Inverse Problems and Imaging, 2010, 4 (3) : 335350. doi: 10.3934/ipi.2010.4.335 
[18] 
Olha P. Kupenko, Rosanna Manzo. On optimal controls in coefficients for illposed nonLinear elliptic Dirichlet boundary value problems. Discrete and Continuous Dynamical Systems  B, 2018, 23 (4) : 13631393. doi: 10.3934/dcdsb.2018155 
[19] 
Faker Ben Belgacem. Uniqueness for an illposed reactiondispersion model. Application to organic pollution in streamwaters. Inverse Problems and Imaging, 2012, 6 (2) : 163181. doi: 10.3934/ipi.2012.6.163 
[20] 
Markus Haltmeier, Antonio Leitão, Otmar Scherzer. Kaczmarz methods for regularizing nonlinear illposed equations I: convergence analysis. Inverse Problems and Imaging, 2007, 1 (2) : 289298. doi: 10.3934/ipi.2007.1.289 
2020 Impact Factor: 1.327
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