American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Positive solutions of superlinear boundary value problems with singular indefinite weight
  • CPAA Home
  • This Issue
  • Next Article
    On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows
September  2003, 2(3): 391-410. doi: 10.3934/cpaa.2003.2.391

On the Lyapunov functions for the solutions of the generalized Burgers equation

Ezzeddine Zahrouni 1,

1. 

Department de Mathematiques, Faculte des Sciences de Monastir , 5000 MONASTIR, Tunisia

Received  October 2002 Revised  April 2003 Published  June 2003

We derive new Lyapunov functions not arising from energy norm for global solutions of Generalized Burgers Equation with initial data in homogeneous Besov spaces.
Keywords: smoothness, Besov spaces, Lyapunov functions., global existence, generalized Burgers equation.
Mathematics Subject Classification: 35K55, 76D03, 35B4.
Citation: Ezzeddine Zahrouni. On the Lyapunov functions for the solutions of the generalized Burgers equation. Communications on Pure & Applied Analysis, 2003, 2 (3) : 391-410. doi: 10.3934/cpaa.2003.2.391
[1]

Shouming Zhou. The Cauchy problem for a generalized $b$-equation with higher-order nonlinearities in critical Besov spaces and weighted $L^p$ spaces. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4967-4986. doi: 10.3934/dcds.2014.34.4967
[2]

Jean-François Rault. A bifurcation for a generalized Burgers' equation in dimension one. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 683-706. doi: 10.3934/dcdss.2012.5.683
[3]

Houyu Jia, Xiaofeng Liu. Local existence and blowup criterion of the Lagrangian averaged Euler equations in Besov spaces. Communications on Pure & Applied Analysis, 2008, 7 (4) : 845-852. doi: 10.3934/cpaa.2008.7.845
[4]

Minghua Yang, Zunwei Fu, Jinyi Sun. Global solutions to Chemotaxis-Navier-Stokes equations in critical Besov spaces. Discrete & Continuous Dynamical Systems - B, 2018, 23 (8) : 3427-3460. doi: 10.3934/dcdsb.2018284
[5]

Peter Giesl, Sigurdur Hafstein. Existence of piecewise linear Lyapunov functions in arbitrary dimensions. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3539-3565. doi: 10.3934/dcds.2012.32.3539
[6]

Long Wei, Zhijun Qiao, Yang Wang, Shouming Zhou. Conserved quantities, global existence and blow-up for a generalized CH equation. Discrete & Continuous Dynamical Systems - A, 2017, 37 (3) : 1733-1748. doi: 10.3934/dcds.2017072
[7]

Oleg Yu. Imanuvilov, Jean Pierre Puel. On global controllability of 2-D Burgers equation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 299-313. doi: 10.3934/dcds.2009.23.299
[8]

Tao Chen, Linda Keen. Slices of parameter spaces of generalized Nevanlinna functions. Discrete & Continuous Dynamical Systems - A, 2019, 39 (10) : 5659-5681. doi: 10.3934/dcds.2019248
[9]

Jerry L. Bona, Laihan Luo. Large-time asymptotics of the generalized Benjamin-Ono-Burgers equation. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 15-50. doi: 10.3934/dcdss.2011.4.15
[10]

Juan Carlos De los Reyes, Estefanía Loayza-Romero. Total generalized variation regularization in data assimilation for Burgers' equation. Inverse Problems & Imaging, 2019, 13 (4) : 755-786. doi: 10.3934/ipi.2019035
[11]

Zhichun Zhai. Well-posedness for two types of generalized Keller-Segel system of chemotaxis in critical Besov spaces. Communications on Pure & Applied Analysis, 2011, 10 (1) : 287-308. doi: 10.3934/cpaa.2011.10.287
[12]

Peter Giesl. Construction of a global Lyapunov function using radial basis functions with a single operator. Discrete & Continuous Dynamical Systems - B, 2007, 7 (1) : 101-124. doi: 10.3934/dcdsb.2007.7.101
[13]

Deqiong Ding, Wendi Qin, Xiaohua Ding. Lyapunov functions and global stability for a discretized multigroup SIR epidemic model. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 1971-1981. doi: 10.3934/dcdsb.2015.20.1971
[14]

Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115
[15]

Minghua Yang, Jinyi Sun. Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces. Communications on Pure & Applied Analysis, 2017, 16 (5) : 1617-1639. doi: 10.3934/cpaa.2017078
[16]

Xiaoping Zhai, Yongsheng Li, Wei Yan. Global well-posedness for the 3-D incompressible MHD equations in the critical Besov spaces. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1865-1884. doi: 10.3934/cpaa.2015.14.1865
[17]

Kotaro Tsugawa. Existence of the global attractor for weakly damped, forced KdV equation on Sobolev spaces of negative index. Communications on Pure & Applied Analysis, 2004, 3 (2) : 301-318. doi: 10.3934/cpaa.2004.3.301
[18]

Yushi Nakano, Shota Sakamoto. Spectra of expanding maps on Besov spaces. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1779-1797. doi: 10.3934/dcds.2019077
[19]

Zijuan Wen, Meng Fan, Asim M. Asiri, Ebraheem O. Alzahrani, Mohamed M. El-Dessoky, Yang Kuang. Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. Mathematical Biosciences & Engineering, 2017, 14 (2) : 407-420. doi: 10.3934/mbe.2017025
[20]

Miao Liu, Weike Wang. Global existence and pointwise estimates of solutions for the multidimensional generalized Boussinesq-type equation. Communications on Pure & Applied Analysis, 2014, 13 (3) : 1203-1222. doi: 10.3934/cpaa.2014.13.1203

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (14)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences