%0 Journal Article
%T Existence of traveling waves for diffusive-dispersive conservation laws
%A Cezar I. Kondo
%A Alex F. Rossini
%J Electronic Journal of Differential Equations
%D 2013
%I Texas State University
%X 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 $y o -infty$. This provides the desired saddle-attractor connection.
%K Scalar conservation law
%K diffusive-dispersive
%K weak solution
%K traveling wave
%K phase portrait
%U http://ejde.math.txstate.edu/Volumes/2013/39/abstr.html