Pointwise estimates on the Green's function for a scalar linear convection-diffusion equation

Journal of Differential Equations

Volumn 155, Issue 2, 1999, Pages 327-367

  Howard, Peter ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033164375     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1998.3576     Document Type: Article

References (34)

1. Alexander J., Gardner R., Jones C. K. R. T. A topological invariant arising in the analysis of traveling waves. J. Reine Angew. Math. 410:1990;167-212.
2. Coppel W. A. Stability and Asymptotic Behavior of Differential Equations. 1965;Heath, Boston.
3. Courant R., Hilbert D. Methods of Mathematical Physics. 1953;Interscience, New York.
4. Evans J. W. Nerve axon equations. I. Linear approximations. Indiana Univ. Math. J. 21:1972;877-885.
5. Evans J. W. Nerve axon equations. II. Stability at rest. Indiana Univ. Math. J. 22:1972;75-90.
6. Evans J. W. Nerve axon equations. III. Stability of the nerve impulse. Indiana Univ. Math. J. 22:1972;577-594.
7. Evans J. W. Nerve axon equations. IV. The stable and unstable impulse. Indiana Univ. Math. J. 24:1975;1169-1190.
8. Friedman A. Partial Differential Equations of Parabolic Type. 1964;Prentice-Hill, Englewood Cliffs.
9. Goodman J. Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rational Mech. Anal. 95:1986;325-344.
10. Gaveau B., Schulman S. Explicit time-dependent Schrödinger propagators. J. Phys. A Math. Gen. 19:1986;1833-1846.
11. Gardner R., Zumbrun K. The Gap Lemma and geometric criteria for instability of viscous shock waves. Comm. Pure Appl. Math. 51:1998;789-847.
12. Howard P. Pointwise Estimates for the Stability of a Scalar Conservation Law. 1998;Indiana University.
13. P. Howard, Pointwise Green's function approach to stability for scalar conservation laws, Comm. Pure Appl. Math, to appear.
14. P. Howard, and, K. Zumbrun, Pointwise estimates and stability for dispersive-diffusive shock waves, preprint, 1999.
15. Hoff D., Zumbrun K. Multi-dimensional diffusion waves for the Navier-Stokes equations of compressible flow. Indiana Univ. Math. J. 44:1995;603-675.
16. Hoff D., Zumbrun K. Pointwise decay estimates for mulidimensional Navier-Stokes diffusion waves. Z. Angew. Math. Phys. 48:1997;597-614.
17. Jones C. K. R. T. Stability of the traveling wave solution of the FitzHugh-Nagumo system. Trans. Amer. Math. Soc. 286:1984;431-469.
18. Jones C. K. R. T., Gardner R., Kapitula T. Stability of travelling waves for nonconvex scalar viscous conservation laws. Comm. Pure Appl. Math. 46:1993;505-526.
19. ∞ spaces. J. Differential Equations. 112:1992;179-215.
20. Pego R. L., Weinstein M. I. Eigenvalues, and instabilities of solitary waves. Philos. Trans. Roy. Soc. London Ser. A. 340:1992;47-94.
21. Liu T. P. Nonlinear stability of shock waves for viscous conservation laws. Mem. Amer. Math. Soc. 56:1985.
22. Liu T. P. Interaction of nonlinear hyperbolic waves. Liu F. C., Liu T. P. Nonlinear Analysis. 1991;171-184 World Scientific, Singapore.
23. Liu T. P. Pointwise convergence to shock waves for the system of viscous conservation laws. Comm. Pure Appl. Math. 50:1997;1113-1182.
24. Liu T. P., Zeng Y. Large time behavior of solutions of general quasilinear hyperbolic-parabolic systems of conservation laws. Mem. Amer. Math. Soc. 599:1997.
25. Liu T. P., Zumbrun K. Nonlinear stability of an undercompressive shock of complex Burgers equation. Comm. Math Phys. 168:1995;163-186.
26. Liu T. P., Zumbrun K. On nonlinear stability of general undercompressive viscous shock waves. Comm. Math. Phys. 174:1995;319-345.
27. Matsumura A., Nishihara K. Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex linearity. Comm. Math. Phys. 165:1994;83-96.
28. Nishihara K. Stability of traveling waves with degenerate shock for systems of one-dimensional viscoelastic model. J. Differential Equations. 120:1995;304-318.
29. Sattinger D. On the stability of waves of nonlinear parabolic systems. Adv. Math. 22:1976;312-355.
30. Szepessy A., Xin Z. Nonlinear stability of viscous shock waves. Arch. Rational Mech. Anal. 122:1993;53-103.
31. Szepessy A., Zumbrun K. Stability of rarefaction waves in viscous media. Arch. Rational Mech. Anal. 133:1996;249-298.
32. Yosida K. Functional Analysis. 1980;Springer-Verlag, New York.
33. 1 asymptotic behavior of compressible, isentropic, viscous 1d flow. Comm. Pure Appl. Math. 47:1994;1053-1092.
34. Zumbrun K., Howard P. Pointwise semigroup methods for and stability of viscous shock waves. Indiana Univ. Math. J. 47:1998.