Skip to main content Accessibility help

Stability theory for quasi-linear wave equations with linear damping

  • R. W. Dickey (a1)


Large time behaviour of solutions to a damped quasi-linear wave equation are studied. Conditions are obtained which guarantee the global existence of a classical solution. The asymptotic behaviour of this solution is studied in the case of a unique equilibrium solution and in the case of multiple equilibria. The results are applied to various special examples.



Hide All
1Courant, R. and Hilbert, D.. Methods of Mathematical Physics, Vol. I (New York: Interscience, 1953).
2Chafee, N. and Infante, E. F.. A bifurcation problem for a nonlinear partial differential equation of parabolic type. Applicable Anal. 4 (1974), 1737.
3Webb, G. F.. A bifurcation problem for a nonlinear hyperbolic partial differential equation. SIAM J. Math. Anal. 10 (1979), 922932.
4Dickey, R. W., Asymptotic behavior of solutions of hyperbolic, semi-linear partial differential equations. J. Math. Anal. Appl. 55 (1976), 380393.
5Zabusky, N. J.. Exact solution for the vibrations of a nonlinear continuous model string. J. Mathematical Phys. 3 (1962), 10281039.
6Lax, P. D.. Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Mathematical Phys. 5 (1964), 611613.
7Courant, R. and Hilbert, D.. Methods of Mathematical Physics, Vol. 2 (New York: Interscience, 1962).
8Coddington, E. A. and Levinson, N.. Theory of Ordinary Differential Equations (New York: McGraw-Hill, 1955).
9Ince, E. L.. Ordinary Differential liquations (New York: Dover, 1956).
10Dickey, R. W.. A quasi-linear evolution equation and the method of Galerkin. Proc. Amer. Math. Soc. 37 (1973), 149156.


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed