Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation

Journal of Evolution Equations

Volumn 4, Issue 1, 2004, Pages 75-97

  Biler, Piotr ^a   Guedda, Mohammed ^b   Karch, Grzegorz ^a  

^a UNIVERSITY OF WROC AW   (Poland)

^b UNIVERSITÉ DE PICARDIE JULES VERNE   (France)

Author keywords

Asymptotic behavior; Selfsimilar solutions; Viscous Hamilton Jacobi equation

Indexed keywords

EID: 1842854674     PISSN: 14243199     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00028-003-0079-x     Document Type: Article

References (29)

1. AMOUR, L., and BEN-ARTZI, M., Global existence and decay for viscous Hamilton-Jacobi equations, Nonlinear Anal. 31 (1998), 621-628.
2. 1 des solutions d'un système parabolique semi-linéaire, C. R. Acad. Sci. Paris, Sér. I Math. 329 (1999), 367-370.
3. BENACHOUR, S. and LAURENÇOT, PH., Global solutions to viscous Hamilton-Jacobi equations with irregular initial data, Comm. Partial Differential Equations 24 (1999), 1999-2021.
4. BENACHOUR, S. and LAURENÇOT, PH., Solutions très singulières d'une équation parabolique non linéaire avec absorption, C. R. Acad. Sci. Paris, Sér. I Math. 328 (1999), 215-220.
5. BENACHOUR, S. and LAURENÇOT, PH., Very singular solutions to a nonlinear parabolic equation with absorption I. Existence, Proc. Roy. Soc. Edinburgh, Sect. A 131 (2001), 27-44.
6. N, Proc. Amer. Math. Soc. 130 (2002), 1103-1111.
7. d, d ≥ 2, J. Funct. Anal. 144 (1997), 301-324.
8. BEN-ARTZI, M., Global existence and decay for a nonlinear parabolic equation, Nonlinear Anal. 19 (1992), 763-768.
9. BEN-ARTZI, M., SOUPLET, P. WEISSLER, F. B., Sur la non-existence et la non-unicité des solutions du problème de Cauchy pour une équation parabolique semi-linéaire, C. R. Acad. Sci. Paris, Sér. I Math. 329 (1999), 371-376.
10. BEN-ARTZI, M. and KOCH, H., Decay of mass for a semilinear parabolic equation, Comm. Partial Differential Equations 24 (1999), 869-881.
11. BILER, P. and KARCH, G., A nonlinear Neumann problem on the half-line, Ann. Polon. Math. 74 (2000), 79-95.
12. BREZIS, H., PELETIER, L. A. and TERMAN, D., A very singular solution of the heat equation with absorption, Arch. Rat. Mech. Anal. 95 (1986), 185-209.
13. CHIPOT, M. and WEISSLER, F. B., Some blowup results for a nonlinear parabolic equation with a gradient term, SIAM J. Math. Anal. 20 (1989), 886-907.
14. DUOANDIKOETXEA, J. and ZUAZUA, E., Moments, masses de Dirac et décomposition de fonctions, C. R. Acad. Sci. Paris, Sér. I Math. 315 (1992), 693-698.
15. GILDING, B., GUEDDA, M. and KERSNER, R., The Cauchy problem for the KPZ equation 1999, preprint.
16. GUEDDA, M., Self-similar solutions to a convection-diffusion processes, Electronic J. Qual. Th. Diff. Eq. 3 (2000), 1-18.
17. GUEDDA, M. and KERSNER, R., Self-similar solutions to the generalized deterministic KPZ equation, 2000, preprint.
18. HERRAIZ, L., Asymptotic behaviour of solutions of some semilinear parabolic problems, Ann. Inst. H. Poincaré-Analyse non linéaire 16 (1999), 49-105.
19. HÖRMANDER, L., "The Analysis of Linear Partial Differential Operators. I; Distribution Theory and Fourier Analysis", Springer-Verlag, Berlin, New York, 1983.
20. KARCH, G., Asymptotics of solutions to a convection-diffusion equation on the half-line, Proc. Roy. Soc. Edinburgh A 130 (2000), 837-853.
21. KARCH, G., Selfsimilar profiles in large time asymptotics of solutions to damped wave equations, Studia Math. 143 (2000), 175-197.
22. KARDAR, M., PARISI, G. and ZHANG, Y. C., Dynamic scaling of growing interfaces, Phys. Rev. Lett. 56 (1986), 889-892.
23. p = 0 as p → +∞, "Evolution equations: existence, regularity and singularities", Warsaw, 1998, 153-161, Banach Center Publ. 52, Polish Acad. Sci., Warsaw, 2000.
24. p = 0 as p → +∞, "Evolution equations: existence, regularity and singularities", Warsaw, 1998, 153-161, Banach Center Publ. 52, Polish Acad. Sci., Warsaw, 2000.
25. PELETIER, L. A. and SERAFINI, H. C., A very singular solution and self-similar solutions of the heat equation with convection, Nonlinear Anal. 24 (1995), 29-49.
26. q, J. Diff. Eq. 165 (2000), 1-23.
27. SNOUSSI, S., TAYACHI, S. and WEISSLER, F. B., Asymptotically self-similar global solutions of a semilinear parabolic equation with a nonlinear gradient term, Proc. Roy. Soc. Edinburgh A 129 (1999), 1291-1307.
28. SOUPLET, P., TAYACHI, S. and WEISSLER, F. B., Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term, Indiana Univ. Math. J. 45 (1996), 655-682.
29. TAYACHI, S., Forward self-similar solutions of a semilinear parabolic equation with a nonlinear gradient term, Diff. Int. Eq. 9 (1996), 1107-1117.