Abstract
We consider an axisymmetric inverse problem for the heat equation inside the cylinder aleq rleq b. We wish to determine the surface temperature on the interior surface {r=a} from the Cauchy data on the exterior surface {r=b}. This problem is ill-posed. Using the Laplace transform, we solve the direct problem. Then the inverse problem is reduced to a Volterra integral equation of the first kind. A standard Tikhonov regularization method is applied to the approximation of this integral equation when the data is not exact. Some numerical examples are given to illustrate the stability of the proposed method.
Highlights
The inverse heat conduction problems (IHCPs) have many applications in different branches of science and technology
A modified Tikhonov regularization method was applied for an axisymmetric backward heat equation in [ ]
In Section, our inverse problem is reduced to the integral equation of Volterra type; we apply the Tikhonov regularization method to compute the boundary temperature u(a, t) = f (t) from the Cauchy data u(b, t) = g(t), ur(b, t) = and give some numerical results
Summary
The inverse heat conduction problems (IHCPs) have many applications in different branches of science and technology. The mollification method and projection regularization based on the Laplace and Fourier transforms are applied respectively in [ ] and [ ]. A modified Tikhonov regularization method was applied for an axisymmetric backward heat equation in [ ]. Lesnic et al [ ] applied the method of fundamental solutions (MFS) (with a Tikhonov regularization) to the radially symmetric inverse heat conduction problem (IHCP) analogous to our problem.
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