Cezar I. Kondo, Alex F. Rossini
Abstract:
In this work we show the existence existence and uniqueness of
traveling waves for diffusive-dispersive 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 right-hand state.
The equilibrium point corresponding to the left-hand state is a
saddle point. According to the phase portrait close to the saddle point,
there are exactly two semi-orbits of the system. We establish that
only one semi-orbit come in the domain of attraction
and converges to
as
.
This provides the desired saddle-attractor connection.
Submitted October 1, 2012. Published February 1, 2013.
Math Subject Classifications: 35L65, 76N10.
Key Words: Scalar conservation law; diffusive-dispersive; 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 13565-905, Sao Carlos - SP, Brazil email: dcik@dm.ufscar.br | |
Alex F. Rossini Federal University of Sao Carlos Department of Mathematics P. O. Box 676 13565-905, Sao Carlos - SP, Brazil email: alexrossini@dm.ufscar.br |
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