American Institute of Mathematical Sciences

Advanced
June  2004, 3(2): 237-252. doi: 10.3934/cpaa.2004.3.237

Regularity of the attractor for kp1-Burgers equation: the periodic case

Mostafa Abounouh 1, and  Olivier Goubet 2,

1. 

Universite Cadi Ayyad, Faculte des Sciences et Techniques, Avenue Abdelkrim Khattabi, BP 549, Marrakech, Morocco
2. 

Universite de Picardie Jules Verne, LAMFA UMR 7352, 33 rue Saint-Leu, 80039 Amiens cedex, France

Received  June 2003 Revised  December 2003 Published  March 2004

We prove the existence of a global attractor for a damped-forced Kadomtsev-Petviashvili equation. We also establish that this equation features an asymptotic smoothing effect. We use energy estimates in conjunction with a suitable splitting of the solutions.
Keywords: Global attractor, asymptotical smoothing effect..
Mathematics Subject Classification: 35Q53, 35B4.
Citation: Mostafa Abounouh, Olivier Goubet. Regularity of the attractor for kp1-Burgers equation: the periodic case. Communications on Pure & Applied Analysis, 2004, 3 (2) : 237-252. doi: 10.3934/cpaa.2004.3.237
[1]

Uchida Hidetake. Analytic smoothing effect and global existence of small solutions for the elliptic-hyperbolic Davey-Stewartson system. Conference Publications, 2001, 2001 (Special) : 182-190. doi: 10.3934/proc.2001.2001.182
[2]

Hongjie Dong. Dissipative quasi-geostrophic equations in critical Sobolev spaces: Smoothing effect and global well-posedness. Discrete & Continuous Dynamical Systems, 2010, 26 (4) : 1197-1211. doi: 10.3934/dcds.2010.26.1197
[3]

Yoshinori Morimoto, Chao-Jiang Xu. Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules. Kinetic & Related Models, 2020, 13 (5) : 951-978. doi: 10.3934/krm.2020033
[4]

Noboru Okazawa, Tomomi Yokota. Smoothing effect for generalized complex Ginzburg-Landau equations in unbounded domains. Conference Publications, 2001, 2001 (Special) : 280-288. doi: 10.3934/proc.2001.2001.280
[5]

Lassaad Aloui, Imen El Khal El Taief. The Kato smoothing effect for the nonlinear regularized Schrödinger equation on compact manifolds. Mathematical Control & Related Fields, 2020, 10 (4) : 699-714. doi: 10.3934/mcrf.2020016
[6]

Khaled El Dika. Smoothing effect of the generalized BBM equation for localized solutions moving to the right. Discrete & Continuous Dynamical Systems, 2005, 12 (5) : 973-982. doi: 10.3934/dcds.2005.12.973
[7]

Ahmet Sahiner, Nurullah Yilmaz, Gulden Kapusuz. A novel modeling and smoothing technique in global optimization. Journal of Industrial & Management Optimization, 2019, 15 (1) : 113-130. doi: 10.3934/jimo.2018035
[8]

Chunqing Wu, Patricia J.Y. Wong. Global asymptotical stability of the coexistence fixed point of a Ricker-type competitive model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3255-3266. doi: 10.3934/dcdsb.2015.20.3255
[9]

Shigui Ruan, Wendi Wang, Simon A. Levin. The effect of global travel on the spread of SARS. Mathematical Biosciences & Engineering, 2006, 3 (1) : 205-218. doi: 10.3934/mbe.2006.3.205
[10]

Wei-Xi Li, Lvqiao Liu. Gelfand-Shilov smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off. Kinetic & Related Models, 2020, 13 (5) : 1029-1046. doi: 10.3934/krm.2020036
[11]

Olivier Goubet. Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 625-644. doi: 10.3934/dcds.2000.6.625
[12]

Eduardo Liz, Gergely Röst. On the global attractor of delay differential equations with unimodal feedback. Discrete & Continuous Dynamical Systems, 2009, 24 (4) : 1215-1224. doi: 10.3934/dcds.2009.24.1215
[13]

I. D. Chueshov, Iryna Ryzhkova. A global attractor for a fluid--plate interaction model. Communications on Pure & Applied Analysis, 2013, 12 (4) : 1635-1656. doi: 10.3934/cpaa.2013.12.1635
[14]

Biyue Chen, Chunxiang Zhao, Chengkui Zhong. The global attractor for the wave equation with nonlocal strong damping. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021015
[15]

Yirong Jiang, Nanjing Huang, Zhouchao Wei. Existence of a global attractor for fractional differential hemivariational inequalities. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1193-1212. doi: 10.3934/dcdsb.2019216
[16]

Hiroshi Matano, Ken-Ichi Nakamura. The global attractor of semilinear parabolic equations on $S^1$. Discrete & Continuous Dynamical Systems, 1997, 3 (1) : 1-24. doi: 10.3934/dcds.1997.3.1
[17]

Yuncheng You. Global attractor of the Gray-Scott equations. Communications on Pure & Applied Analysis, 2008, 7 (4) : 947-970. doi: 10.3934/cpaa.2008.7.947
[18]

Alexey Cheskidov, Susan Friedlander, Nataša Pavlović. An inviscid dyadic model of turbulence: The global attractor. Discrete & Continuous Dynamical Systems, 2010, 26 (3) : 781-794. doi: 10.3934/dcds.2010.26.781
[19]

Rana D. Parshad, Juan B. Gutierrez. On the global attractor of the Trojan Y Chromosome model. Communications on Pure & Applied Analysis, 2011, 10 (1) : 339-359. doi: 10.3934/cpaa.2011.10.339
[20]

Jianhua Huang, Yanbin Tang, Ming Wang. Singular support of the global attractor for a damped BBM equation. Discrete & Continuous Dynamical Systems - B, 2021, 26 (10) : 5321-5335. doi: 10.3934/dcdsb.2020345

2020 Impact Factor: 1.916

Tools

Metrics

  • PDF downloads (34)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences