Symmetry analysis for a fourth-order noise-reduction partial differential equation

被引：2
|
作者：
Leach, P. G. L. [1 ,2 ]
Paliathanasis, Andronikos [1 ,3 ]
机构：
[1] Durban Univ Technol, Inst Syst Sci, POB 1334, ZA-4000 Durban, South Africa
[2] Univ KwaZulu Natal, Sch Math Sci, Durban, South Africa
[3] Univ Austral Chile, Inst Ciencias Fis & Matemat, Valdivia 5090000, Chile
来源：
QUAESTIONES MATHEMATICAE | 2021年 / 44卷 / 11期
基金：
新加坡国家研究基金会;
关键词：
Lie symmetries; noise reduction; image processing; NONLOCAL SYMMETRIES; CONSERVATION-LAWS; LIE; CLASSIFICATION; SL(3; R); SYSTEMS; WAVE;
D O I：
10.2989/16073606.2020.1812009
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
引用
收藏
页码：1541 / 1552
页数：12
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