Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 39, pp. 115.
Existence of traveling waves for diffusivedispersive conservation laws
Cezar I. Kondo, Alex F. Rossini
Abstract:
In this work we show the existence existence and uniqueness of
traveling waves for diffusivedispersive conservation laws with
flux function in
,
by using phase plane analysis.
Also we estimate the domain of attraction of the equilibrium point
attractor corresponding to the righthand state.
The equilibrium point corresponding to the lefthand state is a
saddle point. According to the phase portrait close to the saddle point,
there are exactly two semiorbits of the system. We establish that
only one semiorbit come in the domain of attraction
and converges to
as
.
This provides the desired saddleattractor connection.
Submitted October 1, 2012. Published February 1, 2013.
Math Subject Classifications: 35L65, 76N10.
Key Words: Scalar conservation law; diffusivedispersive; weak solution;
traveling wave; phase portrait.
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Cezar I. Kondo
Federal University of Sao Carlos
Department of Mathematics
P. O. Box 676 13565905, Sao Carlos  SP, Brazil
email: dcik@dm.ufscar.br


Alex F. Rossini
Federal University of Sao Carlos
Department of Mathematics
P. O. Box 676 13565905, Sao Carlos  SP, Brazil
email: alexrossini@dm.ufscar.br

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