Limit set of trajectories of the coupled viscous Burgers' equations

Applied Mathematics Letters

Volumn 11, Issue 1, 1998, Pages 57-61

  Nee, Janpou ^a   Duan, J ^b  

^a INSTITUTE OF MATHEMATICS   (Taiwan)

^b CLEMSON UNIVERSITY   (United States)

Author keywords

Attractor; Burgers' equation; Long time behavior; Phase space analysis; limit set

Indexed keywords

EID: 0041858039     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(97)00133-X     Document Type: Article

References (12)

1. S.E. Esipov, Coupled Burgers equations: A model of polydispersive sedimentation, Phys. Rev. E 52, 3711-3718 (1995).
2. J.M. Burgers, Applications of a model system to illustrate some points of the statistical theory of free turbulence, Proc. Roy. Neth. Acad. Sci. Amsterdam 43, 2-12 (1940).
3. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, (1988).
4. J.K. Hale, Asymptotic Behavior of Dissipative Systems, American Math. Soc., (1988).
5. H.V. Ly, K.D. Mease and E.S. Titi, Some remarks on distributed and boundary control of the viscous Burgers' equation, Numerical Functional Analysis and Optimization (submitted).
6. J.A. Burns and S. Kang, A control problem for Burgers' equation with bounded input/output, Nonlinear Dynamics 2, 235-262 (1991).
7. A.T. Hill and E. Suli, Dynamics of a nonlinear convection-diffusion equation in multidimensional bounded domains, Proc. R. Soc. Edinburgh 125A, 439-448 (1995).
8. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin, (1981).
9. M. Renardy and R.C. Rogers, An Introduction to Partial Differential Equations, Springer-Verlag, New York, (1993).
10. M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, (1974).
11. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York, (1990).
12. W. Walter, Differential and Integral Inequalities, Springer-Verlag, New York, (1970).