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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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Continuous Dynamical Systems  B, 2021 doi: 10.3934/dcdsb.2021142 
[12] 
Rinaldo M. Colombo, Mauro Garavello. A Well Posed Riemann Problem for the $p$System at a Junction. Networks & 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 & 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 & 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 & 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 & 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 & 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 & 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 & 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 & Imaging, 2007, 1 (2) : 289298. doi: 10.3934/ipi.2007.1.289 
2020 Impact Factor: 1.327
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