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http://dx.doi.org/10.4134/JKMS.2011.48.2.311

SIMPLIFIED TIKHONOV REGULARIZATION FOR TWO KINDS OF PARABOLIC EQUATIONS  

Jing, Li (SCHOOL OF MATHEMATICS AND COMPUTATIONAL SCIENCE CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY)
Fang, Wang (SCHOOL OF MATHEMATICS AND COMPUTATIONAL SCIENCE CHANGSHA UNIVERSITY OF SCIENCE AND TECHNOLOGY)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 311-327 More about this Journal
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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