Journal of the
Korean Mathematical Society JKMS

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