BURGERS’ EQUATION WITH VANISHING HYPER-VISCOSITY*

Communications in Mathematical Sciences

Volumn 2, Issue 2, 2004, Pages 317-324

  Tadmor, Eitan ^a  

^a Bldg 142   (United States)

Author keywords

Compensated compactness; Conservation law; Entropy dissipation; Hyper viscosity

Indexed keywords

EID: 33746789536     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2004.v2.n2.a9     Document Type: Article

References (17)

1. [Daf00] C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Springer, 2000.
2. [GT85] D. Gottlieb and E. Tadmor, ecovering pointwise values of discontinuous data with spectral accuracy, in “Progress and Supercomputing in Computational Fluid Dynamics”,( E. M Murman and S.S. Abarbanel eds.), Progress in Scientific Computing, 6:357—375, Birkhauser, Boston, 6:357-375, 1985.
3. [GMT01] B.Y. Guo, H.P. Ma and E. Tadmor, Spectral vanishing viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., 39:1254-1268, 2001.
4. [GO04] L. Giacomelli and F. Otto, New bounds for the Kuramoto-Shivashinsky equation, Comm. Pure Appl. Math., to appear.
5. [LOW04] C. De Lellis, F. Otto, and M. Westdickenberg, Minimal entropy condition for Burgers equation, Quart. Appl. Math., to appear.
6. [KL02] C. Kondo and P. Lefloch, Zero diffusion-dispersion limits for scalar conservation laws, SIMA. 33(6):1320-1329, 2002.
7. [Ma98] H. Ma, Chebyshev-Legendre super spectral viscosity method for nonlinear conservation laws, SINUM 35:893-908, 1998.
8. [MOT93] Y. Maday S.M. Ould Kaber, and E. Tadmor, Legendre pseudospectral viscosity method for nonlinear conservation laws, SIAM J. Numer. Anal., 30:321-342, 1993.
9. [Mur78] F. Murat, “Compacité per compensation”, Ann. Scuola Norm. Sup. Disa Sci. Math., 5:489507, 1978 and 8:69-102, 1981.
10. [NST85] B. Nicolaenko, B. Scheurer, and R. Temam, Some global dynamical properties of the Kuramoto-Sivashinsky equations: Nonlinear stability and attractors, Physica D 16:155—183, 1985.
11. [Pan94] E. Panov, Uniqueness of the solution of the Cauchy problem for a first-order quasilinear equation with an admissible strictly convex entropy, Mat. Zametki, 55(5):116—129, 159, 1994; translation in Math. Notes, 55(5-6):517—525, 1994.
12. [Sch82] M.E. Schonbek, Convergence of solutions to nonlinear dispersive equations, Comm. PDEs., 7(8):959-1000, 1982.
13. [Tad86] E. Tadmor, The well-posedness of the Kuramoto-Sivashinsky equation, SIAM J. Math. Anal., 17:884-893, 1986.
14. [Tad89] E. Tadmor, Convergence of spectral methods for nonlinear conservation laws, SINUM 26:3044, 1989.
15. [Tad93] E. Tadmor, Super viscosity and spectral approximations of nonlinear conservation laws “Numerical Methods for Fluid Dynamics IV”， Proceedings of the 1992 Conference on Numerical Methods for Fluid Dynamics, (M. J. Baines and K. W. Morton, eds.), Clarendon Press, Oxford, 69-82, 1993.
16. [TT02] E. Tadmor and J. Tanner, Adaptive mollifiers - high resolution recovery of piecewise smooth data from its spectral information, Foundations of Comput. Math., 2:155-189, 2002.
17. [Tar75] L. Tartar, Compensated compactness and applications to partial differential equations, in Research Notes in Mathematics 39, Nonlinear Analysis and Mechanics, Heriott-Watt Symposium (R.J. Knopps, ed.), Pittman Press, 4:136-211, 1975.