Geodesic
Existence of traveling waves for diffusive-dispersive conservation laws
Electronic journal of differential equations, Tome 2013 (2013)
In this work we show the existence existence and uniqueness of traveling waves for diffusive-dispersive conservation laws with flux function in $C^{1}(\mathbb{R})$, 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 $(u_{-},0)$ as $y\to -\infty$. This provides the desired saddle-attractor connection.
Classification : 35L65, 76N10
Keywords: scalar conservation law, diffusive-dispersive, weak solution, traveling wave, phase portrait 
@article{EJDE_2013__2013__a19,
     author = {Kondo,  Cezar I. and Rossini,  Alex F.},
     title = {Existence of traveling waves for diffusive-dispersive conservation laws},
     journal = {Electronic journal of differential equations},
     year = {2013},
     volume = {2013},
     zbl = {1288.35165},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a19/}
}
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AU  - Rossini,  Alex F.
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%A Rossini,  Alex F.
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%J Electronic journal of differential equations
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%U http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a19/
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%F EJDE_2013__2013__a19
Kondo,  Cezar I.; Rossini,  Alex F. Existence of traveling waves for diffusive-dispersive conservation laws. Electronic journal of differential equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a19/