Existence of solutions for quasilinear problem with Neumann boundary conditions
DOI:
https://doi.org/10.5269/bspm.46956Abstract
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.
References
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10. J. L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod, Paris, (1969).
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12. A. Moussaoui, B. Khodja, Existence results for a class of semilinear elliptic systems, Journal of Partial Differential Equations, 22, 111-126, (2009).
13. 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
14. 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
2. 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
3. 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
4. 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
5. 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).
6. H. Lakhal, B. Khodja, Elliptic systems at resonance for jumping non-linearities, Electronic Journal of Differential Equations, N 70, 1-13, (2016).
7. 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.
8. 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.
9. 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.
10. J. L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires, Dunod, Paris, (1969).
11. 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
12. A. Moussaoui, B. Khodja, Existence results for a class of semilinear elliptic systems, Journal of Partial Differential Equations, 22, 111-126, (2009).
13. 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
14. 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
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2021-12-20
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