Symmetry Analysis for a Fourth-order Noise-reduction Partial Differential Equation

DOI10.2989/16073606.2020.1812009arXiv2008.06323WikidataQ114039700 ScholiaQ114039700MaRDI QIDQ6347086

P. G. L. Leach, Andronikos Paliathanasis

Publication date: 14 August 2020

Abstract: We apply the theory of Lie symmetries in order to study a fourth-order $1+2$ evolutionary partial differential equation which has been proposed for the image processing noise reduction. In particular we determine the Lie point symmetries for the specific 1+2 partial differential equations and we apply the invariant functions to determine similarity solutions. For the static solutions we observe that the reduced fourth-order ordinary differential equations are reduced to second-order ordinary differential equations which are maximally symmetric. Finally, nonstatic closed-form solutions are also determined.

Mathematics Subject Classification ID

Nonlinear evolution equations (47J35) Other special methods applied to PDEs (35A25) Classical solutions to PDEs (35A09)

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