Diffusive N-waves and metastability in the burgers equation

SIAM Journal on Mathematical Analysis

Volumn 33, Issue 3, 2001, Pages 607-633

  Kim, Yong Jung ^a   Tzavaras, Athanasios E ^b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Convection diffusion; Diffusion waves; Diffusive N waves; Metastability

Indexed keywords

EID: 0036347961     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141000380516     Document Type: Article

References (21)

1. S. ANGENENT, The zero set of a solution of a parabolic equation, J. Reine Angew. Math., 390 (1988), pp. 79-96.
2. C. M. DAFERMOS, Generalized characteristics and the structure of solutions of hyperbolic conservation laws, Indiana Univ. Math. J., 26 (1977), pp. 1097-1119.
3. C. M. DAFERMOS, Asymptotic behavior of solutions of evolution equations, in Nonlinear Evolution Equations, M. G. Crandall, ed., Academic Press, New York, 1978, pp. 103-124.
4. C. M. DAFERMOS, Hyperbolic Conservation Laws in Continuum Physics, Springer-Verlag, New York, 2000.
5. N, J. Funct. Anal., 100 (1991), pp. 119-161.
6. M. ESCOBEDO, J. L. VAZQUEZ, AND E. ZUAZUA, Asymptotic behaviour and source-type solutions for a diffusion-convection equation, Arch. Ration. Mech. Anal., 124 (1993), pp. 43-65.
7. xx, Comm. Pure Appl. Math., 3 (1950), pp. 201-230.
8. S. N. KRUZHKOV, First order quasilinear equations in several independent variables, Math. USSR Sb. 10 (1970), pp. 217-243.
9. S. N. KRUZHKOV, Quasilineare Gleichungen erster Ordnung mit mehreren unabhaengigen Veraenderlichen, Mat. Sb., 123 (1970), pp. 228-255.
10. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Lectures in Mathematics ETH Zürich, Birkhäuser-Verlag, Basel, 1990.
11. G. LIEBERMAN, Second Order Parabolic Differential Equations, World Scientific, River Edge, NJ, 1996.
12. T.-P. LIU, Invariants and asymptotic behavior of solutions of a conservation law, Proc. Amer. Math. Soc., 71 (1978), pp. 227-231.
13. T.-P. LIU AND M. PIERRE, Source-solutions and asymptotic behavior in conservation laws, J. Differential Equations, 51 (1984), pp. 419-441.
14. T.-P. LIU, A. MATSUMURA, AND K. NISHIHARA, Behaviors of solutions for the Burgers equation with boundary corresponding to rarefaction waves, SIAM J. Math. Anal., 29 (1998), pp. 293-308.
15. H. MATANO, Nonincrease of the lap number of a solution for a one-dimensional semi-linear parabolic equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 29 (1982), pp. 401-441.
16. O. OLEINIK, Discontinuous solutions of nonlinear differential equations, Uspekhi Mat. Nauk (N.S.), 12 (1957), pp. 3-73 (in Russian).
17. O. OLEINIK, Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Transl. (2), 26 (1963), pp. 95-172.
18. D. H. SATTINGER, On the total variation of solutions of parabolic equations, Math. Ann., 183 (1969), pp. 78-92.
19. G. SZEGÖ, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ. 23, AMS, Providence, RI, 1939.
20. L. TARTAR, Une introduction a la théorie matheématique des systèmes hyperboliques de lois de conservation, Pubblicazioni CNR Instituto di Analisi Numerica, 682, Pavia, Italy, 1989.
21. G. WHITHAM, Linear and Nonlinear Waves, Pure Appl. Math., Wiley Interscience, New York, 1974.