Comptes Rendus
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

Jacson Simsen1
1 Instituto de Matemática e Computação, Universidade Federal de Itajubá, Av. BPS n. 1303, Bairro Pinheirinho, 37500-903, Itajubá, MG, Brazil
Comptes Rendus. Mathématique, Volume 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
Jacson Simsen 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 = {Jacson Simsen},
     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},
}
TY  - JOUR
AU  - Jacson Simsen
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
DO  - 10.1016/j.crma.2013.02.009
LA  - en
ID  - CRMATH_2013__351_3-4_87_0
ER  - 
%0 Journal Article
%A Jacson Simsen
%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
%R 10.1016/j.crma.2013.02.009
%G en
%F CRMATH_2013__351_3-4_87_0
Jacson Simsen. 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://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.009/

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

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

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

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

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

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

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

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

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

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

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

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

[15] J. Simsen; M.S. Simsen 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] L. Songzhe; G. Wenjie; C. Chunling; Y. Hongjun 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 :

Commentaires - Politique