# A modified Tikhonov regularization method for an axisymmetric backward heat equation

## Related Articles

- A Meshless Method Based on the Fundamental Solution and Radial Basis Function for Solving an Inverse Heat Conduction Problem. Arghand, Muhammad; Amirfakhrian, Majid // Advances in Mathematical Physics;4/14/2015, Vol. 2015, p1
We propose a new meshless method to solve a backward inverse heat conduction problem. The numerical scheme, based on the fundamental solution of the heat equation and radial basis functions (RBFs), is used to obtain a numerical solution. Since the coefficients matrix is ill-conditioned, the...

- Inverse Estimates for Nonhomogeneous Backward Heat Problems. Tao Min; Weimin Fu; Qiang Huang // Journal of Applied Mathematics;2014, p1
We investigate the inverse problem in the nonhomogeneous heat equation involving the recovery of the initial temperature from measurements of the final temperature. This problem is known as the backward heat problem and is severely ill-posed. We showthat this problem can be converted into the...

- Tikhonov regularization for illâ€posed backward nonlinear Maxwell's equations. Chen, De‐Han; Yousept, Irwin // PAMM: Proceedings in Applied Mathematics & Mechanics;Dec2018, Vol. 18 Issue 1, p1
Tikhonov regularization for illâ€posed backward nonlinear Maxwell's equations is considered. We present a convergence result with rate for the Tikhonov regularization under piecewise Hsâ€type Sobolev regularity assumption on the exact initial data.

- Regular solution of inverse optimal design problems for axisymmetric systems of radiative heat transfer. Rukolaine, S. // High Temperature;Jan2008, Vol. 46 Issue 1, p115
Inverse optimal design problems are considered for axisymmetric systems of heat transfer with only radiative heat transfer. In these problems, the geometry of thermal system is preassigned, and it is required to find the optimal distribution of temperature on the heater surface, which provides...

- An improved stability result for a heat equation backward in time with nonlinear source. Nguyen Huy Tuan; Pham Hoang Quan // Mathematical Communications;2012, Vol. 17 Issue 1, p113
We consider a nonlinear backward heat conduction problem in a strip. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. We shall use a modified integral equation method to regularize the nonlinear problem. The error estimates of...

- Mathematical and numerical modeling of inverse heat conduction problem. DANAILA, Sterian; CHIRA, Alina-Ioana // INCAS Bulletin;2014, Vol. 6 Issue 4, p23
The present paper refers to the assessment of three numerical methods for solving the inverse heat conduction problem: the Alifanov's iterative regularization method, the Tikhonov local regularization method and the Tikhonov equation regularization method, respectively. For all methods we...

- A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation. Jinghuai Gao; Dehua Wang; Jigen Peng // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1
An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical...

- A Tikhonov-Type Regularization Method for Identifying the Unknown Source in the Modified Helmholtz Equation. Jinghuai Gao; Dehua Wang; Jigen Peng // Mathematical Problems in Engineering;2012, Vol. 2012, Special section p1
An inverse source problem in the modified Helmholtz equation is considered. We give a Tikhonov-type regularization method and set up a theoretical frame to analyze the convergence of such method. A priori and a posteriori choice rules to find the regularization parameter are given. Numerical...

- Identifying an unknown source in the Poisson equation by a modified Tikhonov regularization method. Ou Xie; Zhenyu Zhao // World Academy of Science, Engineering & Technology;2012, Issue 68, p592
In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find...