Spectral Properties of Solutions of the Burgers Equation with Small Dissipation

Functional Analysis and its Applications

Volumn 35, Issue 1, 2001, Pages 1-12

  Biryuk, A e ^a,b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035639812     PISSN: 00162663     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1004143415090     Document Type: Article

References (12)

1. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasi-Linear Equations of Parabolic Type, Amer. Math. Soc., Providence, R.I., 1968.
2. S. N. Kruzhkov, "First order quasilinear equations in several independent variables," Mat. Sb., 81 (123), No. 2, 228-255 (1970); English transl. Math USSR-Sb., 10, 217-243 (1970).
3. S. N. Kruzhkov, "First order quasilinear equations in several independent variables," Mat. Sb., 81 (123), No. 2, 228-255 (1970); English transl. Math USSR-Sb., 10, 217-243 (1970).
4. N. N. Kuznecov, "The accuracy of some approximate methods for computing weak solutions of a first order quasilinear equation," Zh. Vychisl. Mat. i Mat. Fiz., 16, No. 6, 1489-1502 (1976); English transl. USSR Comp. Math, and Math. Phys., 16, No. 6, 105-119 (1976).
5. N. N. Kuznecov, "The accuracy of some approximate methods for computing weak solutions of a first order quasilinear equation," Zh. Vychisl. Mat. i Mat. Fiz., 16, No. 6, 1489-1502 (1976); English transl. USSR Comp. Math, and Math. Phys., 16, No. 6, 105-119 (1976).
6. A. N. Kolmogorov, "On inequalities for supremums of successive derivatives of a function on an infinite interval," In: Selected works of A. N. Kolmogorov, Vol. 1, Kluwer, 1991.
7. L. Hörmander, Lectures on Nonlinear Hyperbolic Differential Equations, Springer-Verlag, Berlin, 1997.
8. P. D. Lax, "Hyperbolic systems of conservation laws II," Comm. Pure Appl. Math., 10, 537-566 (1957).
9. A. N. Kolmogorov and S. V. Fomin, Introductory Real Analysis, Dover Publ., New York, 1975.
10. U. Frish, Turbulence. The Legacy of A. N. Kolmogorov, Cambridge Univ. Press, 1995.
11. S. Kuksin, "Spectral Properties of Solutions for Nonlinear PDE's in the Turbulent Regime, Geom. Funct. Anal., 9, 141-184 (1999).
12. Weinan E, K. Khanin, A. Mazel, and Ya. Sinai, "Invariant measures for Burgers equation with stochastic forcing," Ann. of Math., 151, No. 3, 877-960 (2000).