# SIMPLIFIED TIKHONOV REGULARIZATION FOR TWO KINDS OF PARABOLIC EQUATIONS

• Jing, Li ;
• Fang, Wang
• Published : 2011.03.01
• 52 7

#### Abstract

This paper is devoted to simplified Tikhonov regularization for two kinds of parabolic equations, i.e., a sideways parabolic equation, and a two-dimensional inverse heat conduction problem. The measured data are assumed to be known approximately. We concentrate on the convergence rates of the simplified Tikhonov approximation of u(x, t) and its derivative $u_x$(x, t) of sideways parabolic equations at 0 $\leq$ x < 1, and that of two-dimensional inverse heat conduction problem at 0 < x $\leq$ 1, respectively.

#### Keywords

Fourier transformation;simplified Tikhonov regularization;convergence rate;sideways parabolic equations;inverse heat conduction problems

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#### Cited by

1. A Modified Kernel Method for Solving Cauchy Problem of Two-Dimensional Heat Conduction Equation vol.7, pp.01, 2015, https://doi.org/10.4208/aamm.12-m12113
2. A Revised Tikhonov Regularization Method for a Cauchy Problem of Two-Dimensional Heat Conduction Equation vol.2018, pp.1563-5147, 2018, https://doi.org/10.1155/2018/1216357

#### Acknowledgement

Supported by : NNSF of China, Hunan Provincial Natural Science Foundation of China