no. 3-4
Mathematical Analysis/Partial Differential Equations
A global attractor for a p(x)-Laplacian inclusion
[Un attracteur global dʼune inclusion avec p(x)-Laplacien]

Présenté par : Jean-Michel Bony

Simsen, Jacson1
1 Instituto de Matemática e Computação, Universidade Federal de Itajubá, Av. BPS n. 1303, Bairro Pinheirinho, 37500-903, Itajubá, MG, Brazil
Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 87-90.

Dans ce travail, nous prouvons lʼexistence dʼun attracteur global dʼune inclusion avec p(x)-Laplacien de la forme ∂u∂t−div(|∇u|p(x)−2∇u)+α|u|p(x)−2u∈F(u)+h, α=0,1.

In this work we prove the existence of a global attractor for a p(x)-Laplacian inclusion of the form ∂u∂t−div(|∇u|p(x)−2∇u)+α|u|p(x)−2u∈F(u)+h, α=0,1.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.009
Simsen, Jacson 1

1 Instituto de Matemática e Computação, Universidade Federal de Itajubá, Av. BPS n. 1303, Bairro Pinheirinho, 37500-903, Itajubá, MG, Brazil 
@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 = {http://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  - http://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  - 
%0 Journal Article
%A Simsen, Jacson
%T A global attractor for a $ p(x)$-Laplacian inclusion
%J Comptes Rendus. Mathématique
%D 2013
%P 87-90
%V 351
%N 3-4
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2013.02.009/
%R 10.1016/j.crma.2013.02.009
%G en
%F CRMATH_2013__351_3-4_87_0
Simsen, Jacson. A global attractor for a $ p(x)$-Laplacian inclusion. Comptes Rendus. Mathématique, Tome 351 (2013) no. 3-4, pp. 87-90. doi : 10.1016/j.crma.2013.02.009. http://www.numdam.org/articles/10.1016/j.crma.2013.02.009/

[1] Aboulaich, R.; Meskine, D.; Souissi, A. New diffusion models in image processing, Comput. Math. Appl., Volume 56 (2008), pp. 874-882

[2] Antonstev, S.N.; Shmarev, S.I. 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] Antontsev, S.N.; Shmarev, S. 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] Chen, Y.; Levine, S.; Rao, M. Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., Volume 66 (2006) no. 4, pp. 1383-1406

[5] Diening, L.; Harjulehto, P.; Hästö, P.; Růžička, M. Lebesgue and Sobolev Spaces with Variable Exponents, Springer-Verlag, Berlin, Heidelberg, 2011

[6] Guo, Z.; Liu, Q.; Sun, J.; Wu, B. Reaction–diffusion systems with p(x)-growth for image denoising, Nonlinear Anal. Real World Appl., Volume 12 (2011), pp. 2904-2918

[7] Harjulehto, P.; Hästö, P.; Lê, U.; Nuortio, M. Overview of differential equations with non-standard growth, Nonlinear Anal., Volume 72 (2010), pp. 4551-4574

[8] Melnik, V.S.; Valero, J. On attractors of multivalued semi-flows and differential inclusions, Set-Valued Anal., Volume 6 (1998), pp. 83-111

[9] Niu, W. Long-time behavior for a nonlinear parabolic problem with variable exponents, J. Math. Anal. Appl., Volume 393 (2012), pp. 56-65

[10] Rajagopal, K.; Růžička, M. Mathematical modelling of electrorheological fluids, Contin. Mech. Thermodyn., Volume 13 (2001), pp. 59-78

[11] Růžička, M. Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math., vol. 1748, Springer-Verlag, Berlin, 2000

[12] Simsen, J. A global attractor for a p(x)-Laplacian problem, Nonlinear Anal., Volume 73 (2010), pp. 3278-3283

[13] Simsen, J.; Simsen, M.S. PDE and ODE limit problems for p(x)-Laplacian parabolic equations, J. Math. Anal. Appl., Volume 383 (2011), pp. 71-81

[14] Simsen, J.; Simsen, M.S. On p(x)-Laplacian parabolic problems, Nonlinear Stud., Volume 18 (2011) no. 3, pp. 393-403

[15] Simsen, J.; Simsen, M.S. Existence and upper semicontinuity of global attractors for p(x)-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] Songzhe, L.; Wenjie, G.; Chunling, C.; Hongjun, Y. 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

Cité par Sources :