Title: New exact solutions to nonlinear diffusion equation that occurs in image processing

Authors: Rafaa Chouder; Nouredine Benhamidouche

Addresses: Laboratory for Pure and Applied Mathematics, University of M'sila, Bp 166 M'sila, 28000, Algeria ' Laboratory for Pure and Applied Mathematics, University of M'sila, Bp 166 M'sila, 28000, Algeria

Abstract: In this paper, we would like to seek the new exact solutions to nonlinear diffusion equation that occurs in image processing. This equation is called degenerate parabolic equation. The solutions which we seek are called 'travelling profiles solutions'. For that, we have used the 'travelling profiles method' in order to find, explicitly, new exact solutions to this equation under some conditions. An interesting particular case has been discussed, this case coincides with particular solutions called 'intermediate asymptotic solutions' used to study the contour enhancement in image processing.

Keywords: nonlinear diffusion; travelling profile solutions; exact solutions; contour enhancement; image processing.

DOI: 10.1504/IJCSM.2019.102690

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.4, pp.364 - 374

Received: 11 May 2017
Accepted: 03 Aug 2017
Published online: 02 Oct 2019 *

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