Please use this identifier to cite or link to this item:
Title: Determination of the time-dependent thermal grooving coefficient
Authors: Cao, Kai
Lesnic, Daniel
Ismailov, Mansur I.
Keywords: inverse problems
fourth-order parabolic equation
thermal grooving coefficient
predictor-corrector method
Issue Date: 2021
Publisher: Journal of Applied Mathematics and Computing
Series/Report no.: Vol. 65;
Abstract: Changes in morphology of a polycrystalline material may occur through interface motion under the action of a driving force. An important special case that is considered in this paper is the thermal grooving that occurs when a grain boundary intersects the flat surface of a recently solidified metal slab giving rise to the formation of a thin symmetric groove. In case the transient surface diffusion is the main forming mechanism this yields a fourth-order time-dependent partial differential equation with unknown time-dependent surface diffusivity. In order to determine it, the profile of the free grooving surface at a fixed location is recorded in time. The grooving boundaries are supported by self-adjoint boundary conditions. We provide sufficient conditions on the input data for which the resulting coefficient identification problem is proved to be well-posed. Furthermore, we develop a predictor-corrector finite-difference spline method for obtaining an accurate and stable numerical solution to the nonlinear coefficient identification problem. Numerical results illustrate the performance of the inversion of both exact and noisy data.
Appears in Collections:Publication

Files in This Item:
File Description SizeFormat 
Determination of the time-dependent thermal grooving coefficient.pdf653.23 kBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.