In this work we prove the existence of a global attractor for a -Laplacian inclusion of the form , .
Dans ce travail, nous prouvons lʼexistence dʼun attracteur global dʼune inclusion avec -Laplacien de la forme , .
Accepted:
Published online:
@article{CRMATH_2013__351_3-4_87_0, author = {Simsen, Jacson}, title = {A global attractor for a $ p(x)${-Laplacian} inclusion}, journal = {Comptes Rendus. Math\'ematique}, pages = {87--90}, publisher = {Elsevier}, volume = {351}, number = {3-4}, year = {2013}, doi = {10.1016/j.crma.2013.02.009}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.crma.2013.02.009/} }
TY - JOUR AU - Simsen, Jacson TI - A global attractor for a $ p(x)$-Laplacian inclusion JO - Comptes Rendus. Mathématique PY - 2013 SP - 87 EP - 90 VL - 351 IS - 3-4 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2013.02.009/ DO - 10.1016/j.crma.2013.02.009 LA - en ID - CRMATH_2013__351_3-4_87_0 ER -
Simsen, Jacson. A global attractor for a $ p(x)$-Laplacian inclusion. Comptes Rendus. Mathématique, Volume 351 (2013) no. 3-4, pp. 87-90. doi : 10.1016/j.crma.2013.02.009. https://www.numdam.org/articles/10.1016/j.crma.2013.02.009/
[1] New diffusion models in image processing, Comput. Math. Appl., Volume 56 (2008), pp. 874-882
[2] A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions, Nonlinear Anal., Volume 60 (2005), pp. 515-545
[3] Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity, J. Math. Sci., Volume 150 (2008) no. 5, pp. 2289-2301
[4] Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., Volume 66 (2006) no. 4, pp. 1383-1406
[5] Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin, Heidelberg, 2011
[6] Reaction–diffusion systems with -growth for image denoising, Nonlinear Anal. Real World Appl., Volume 12 (2011), pp. 2904-2918
[7] Overview of differential equations with non-standard growth, Nonlinear Anal., Volume 72 (2010), pp. 4551-4574
[8] On attractors of multivalued semi-flows and differential inclusions, Set-Valued Anal., Volume 6 (1998), pp. 83-111
[9] Long-time behavior for a nonlinear parabolic problem with variable exponents, J. Math. Anal. Appl., Volume 393 (2012), pp. 56-65
[10] Mathematical modelling of electrorheological fluids, Contin. Mech. Thermodyn., Volume 13 (2001), pp. 59-78
[11] Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., vol. 1748, Springer-Verlag, Berlin, 2000
[12] A global attractor for a -Laplacian problem, Nonlinear Anal., Volume 73 (2010), pp. 3278-3283
[13] PDE and ODE limit problems for -Laplacian parabolic equations, J. Math. Anal. Appl., Volume 383 (2011), pp. 71-81
[14] On -Laplacian parabolic problems, Nonlinear Stud., Volume 18 (2011) no. 3, pp. 393-403
[15] Existence and upper semicontinuity of global attractors for -Laplacian systems, J. Math. Anal. Appl., Volume 388 (2012), pp. 23-38
[16] J. Simsen, M.S. Simsen, F.B. Rocha, Existence of solutions for some classes of parabolic problems involving variable exponents, 2012, submitted for publication.
[17] Study of the solutions to a model porous medium equation with variable exponent of nonlinearity, J. Math. Anal. Appl., Volume 342 (2008), pp. 27-38
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