Existence of solutions for quasilinear problem with Neumann boundary conditions
Resumo
This paper is devoted to the study of the existence of weak solutions for quasilinear systems of a partial dierential equations which are the combination of the Perona-Malik equation and the Heat equation. The proof of the main results are based on the compactness method and the motonocity arguments.
Downloads
Referências
A. Atlas, F. Karami, D. Meskine, The Perona-Malik inequality and application to image denoising, Nonlinear Analysis: Real World Applications, 18, 57-68, (2014). https://doi.org/10.1016/j.nonrwa.2013.11.006
M. Biegert, M. Warma, The heat equation with nonlinear generalized Robin boundary conditions, J. Differential Equations, 247, 1949-1979, (2009). https://doi.org/10.1016/j.jde.2009.07.017
Th. Gallouet, O. Kavian, Resultats d'existence et de non-existence pour certains problemes demi-lineares a l'infini, Ann. Fac. Sci. de Toulouse Math, 5(3), 201-246, (1981). https://doi.org/10.5802/afst.568
P. Guidotti, A bakward-forward regularization of the Perona-Malik equation, J. Differential Equations 252(4), 3226-3244, (2012). https://doi.org/10.1016/j.jde.2011.10.022
H. Lakehal, B. Khodja, W. Gharbi, Existence results of nontrivial solutions for a semi linear elliptic system at resonance, Journal of Advanced Research in Dynamical and Control Systems, 5(3), 1-12, (2013).
H. Lakhal, B. Khodja, Elliptic systems at resonance for jumping non-linearities, Electronic Journal of Differential Equations, N 70, 1-13, (2016).
S. Lecheheb, M. Maouni, H. Lakhal, Existence of the solution of a quasilinear equation and its application to image denoising, International Journal of Computer Science, Computer Science, Communication and Information Technology (CSCIT) 7 (2), 1-6, 2019.
S. Lecheheb, M. Maouni, H. Lakhal, Image restoration using nonlinear elliptic Equaion, International Journal of Computer Science, Computer Science, Communication and Information Technology (CSCIT) 6 (2), 32-37, 2019.
S. Lecheheb, H. Lakhal, M. Maouni, K. Slimani, Study of a system of Diffusion-Convection-Reaction, International Journal of Partial Differential Equations and Applications. 4(2), 32-37, 2016.
J. L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod, Paris, (1969).
A. Moussaoui and J. Velin, Existence and a priori estimates of solutions for quasilinear singular elliptic systems with variable exponents, Journal of Elliptic and Parabolic Equations, 4 (2), 417-440, (2018) https://doi.org/10.1007/s41808-018-0025-2
A. Moussaoui, B. Khodja, Existence results for a class of semilinear elliptic systems, Journal of Partial Differential Equations, 22, 111-126, (2009).
V. Kamalaveni, R. Anitha Rajalakshmi, K. A. Narayanankutty, Image Denoising using Variations of Perona-Malik Model with different Edge Stopping Functions, Procedia Computer Science 58, 673-682, (2015). https://doi.org/10.1016/j.procs.2015.08.087
Y. Q. Wang, Jichang Guo, Wufan Chen, Wenxue Zhang, Image denoising using Modified Perona-Malik Model based on Directional Laplacian, Signal Processing, 93, 2548-2558, (2013). https://doi.org/10.1016/j.sigpro.2013.02.020
Copyright (c) 2021 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
