Access the full text.
Sign up today, get DeepDyve free for 14 days.
B. Yildiz, Hakan Yetiskin, Ali Sever (2003)
A stability estimate on the regularized solution of the backward heat equationAppl. Math. Comput., 135
M. Klibanov (2015)
Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEsInverse Problems, 31
N. Tuan (2013)
Stability estimates for a class of semi-linear ill-posed problemsNonlinear Analysis-real World Applications, 14
N. Tuan, D. Trong, P. Quan (2010)
On a backward Cauchy problem associated with continuous spectrum operatorNonlinear Analysis-theory Methods & Applications, 73
LiuJijun (2003)
CONTINUOUS DEPENDENCE FOR A BACKWARD PARABOLIC PROBLEM, 16
D. Hào, N. Duc, D. Lesnic (2010)
Regularization of parabolic equations backward in time by a non-local boundary value problem methodIma Journal of Applied Mathematics, 75
Jin Cheng, Jin Cheng, Jijun Liu (2008)
A quasi Tikhonov regularization for a two-dimensional backward heat problem by a fundamental solutionInverse Problems, 24
Nguyen Oanh (2013)
A splitting method for a backward parabolic equation with time-dependent coefficientsComput. Math. Appl., 65
M. Klibanov, Andrey Kuzhuget, Kirill Golubnichiy (2015)
An ill-posed problem for the Black–Scholes equation for a profitable forecast of prices of stock options on real market dataInverse Problems, 32
M. Klibanov (2014)
Carleman estimates for the regularization of ill-posed Cauchy problemsApplied Numerical Mathematics, 94
N. Tuan, D. Trong (2010)
Sharp estimates for approximations to a nonlinear backward heat equationNonlinear Analysis-theory Methods & Applications, 73
Matthew Fury (2013)
MODIFIED QUASI-REVERSIBILITY METHOD FOR NONAUTONOMOUS SEMILINEAR PROBLEMS
E. Fernández-Cara, E. Zuazua (2000)
The cost of approximate controllability for heat equations: the linear caseAdvances in Differential Equations
Beth Hetrick, R. Hughes (2009)
Continuous dependence on modeling for nonlinear ill-posed problemsJournal of Mathematical Analysis and Applications, 349
M. Denche, K. Bessila (2005)
A modified quasi-boundary value method for ill-posed problemsJournal of Mathematical Analysis and Applications, 301
M. Klibanov, N. Koshev, Jingzhi Li, A. Yagola (2016)
Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight functionJournal of Inverse and Ill-posed Problems, 24
M.A. Fury (2013)
Proceedings of the Ninth MSU-UAB Conference on Differential Equations and Computational Simulations
M. Nair, S. Pereverzev, U. Tautenhahn (2005)
Regularization in Hilbert scales under general smoothing conditionsInverse Problems, 21
N. Tuan, P. Quan (2011)
Some extended results on a nonlinear ill-posed heat equation and remarks on a general case of nonlinear termsNonlinear Analysis-real World Applications, 12
P. Nam (2010)
An approximate solution for nonlinear backward parabolic equationsJournal of Mathematical Analysis and Applications, 367
M. Klibanov, A. Timonov (2004)
Carleman estimates for coefficient inverse problems and numerical applications
N. Tuan, D. Trong (2010)
A nonlinear parabolic equation backward in time: Regularization with new error estimatesNonlinear Analysis-theory Methods & Applications, 73
B. Johansson, D. Lesnic, T. Reeve (2011)
A comparative study on applying the method of fundamental solutions to the backward heat conduction problemMath. Comput. Model., 54
N. Boussetila, F. Rebbani (2007)
A Modified Quasi-Reversibility Method for a Class of Ill-Posed Cauchy Problems, 14
G. Clark, S. Oppenheimer (1994)
Quasireversibility Methods for Non-Well-Posed ProblemsElectronic Journal of Differential Equations, 1994
We study the backward problem for non-linear (semilinear) parabolic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak a priori assumption on the exact solution, we propose a new Fourier truncated regularization method for stabilising the ill-posed problem. In comparison with previous studies on solving the nonlinear backward problem, our method shows a significant improvement.
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 31, 2016
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.