Stability estimates and regularization for an inverse heat conduction prolem in semi - infinite and finite time intervals
- 1 January 1989
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 10 (5-6) , 517-540
- https://doi.org/10.1080/01630568908816316
Abstract
The problem of determining the temperature or the heat flux on one end of an interval from temperature measurements on the (insulated) other end is ill-posed. For the cases of a semi-infinite or finite time - interval, we obtain stability estimates of logarithmic type under simple a-priori assumptions. If we assume more smoothness, we obtain stability estimates of Hölder type via Tikhonov regularization.Keywords
This publication has 11 references indexed in Scilit:
- A posteriori parameter choice for general regularization methods for solving linear ill-posed problemsApplied Numerical Mathematics, 1988
- A parameter choice strategy for (iterated) tikhonov regularization of iii-posed problems leading to superconvergence with optimal ratesApplicable Analysis, 1988
- The Linear Functional Strategy for Improperly Posed ProblemsPublished by Springer Nature ,1986
- Numerical solution of an inverse problem connected with continuous casting of steelMathematical Methods of Operations Research, 1985
- Optimal Discrepancy Principles for the Tikh0n0v Regularization of Integral Equations of the First KindPublished by Springer Nature ,1985
- On the Convergence of Regularization Methods for Ill-Posed Linear Operator EquationsPublished by Springer Nature ,1983
- The Mollification Method and the Numerical Solution of an Inverse Heat Conduction ProblemSIAM Journal on Scientific and Statistical Computing, 1981
- Necessary and sufficient conditions for convergence of regularization methods for solving linear operator equations of the first kindNumerical Functional Analysis and Optimization, 1981
- Calculation of the surface temperature and heat flux on one side of a wall from measurements on the opposite sideAnnali di Matematica Pura ed Applicata (1923 -), 1980
- Regularization with differential operators. I. General theoryJournal of Mathematical Analysis and Applications, 1980