Qualitative behavior of conservation laws with reaction term and nonconvex flux

Qualitative Behavior of Conservation Laws with Reaction Term and Nonconvex Flux

The aim of the paper is to study qualitative behavior of solutions to the equation du df(u) , . m + ~oT9(o)' where (x,t) £lx R+,u = u(x,t) € R. The main new feature with respect to previous works is that the flux function / may have finitely many inflection points, intervals in which it is afEne, and corner points. The function g is supposed to be zero at 0 and 1, and positive in between. We pr...

Conservation laws with discontinuous flux

We consider an hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applicative problems, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions...

A Nonconvex Scalar Conservation Law with Trilinear Flux

The focus of this paper is on traveling wave solutions of the equation u t + f(u) x = u xx + 2 u xxx ; in which the ux function f is trilinear and nonconvex. In particular, it is shown that for combinations of parameters in certain ranges, there are traveling waves that converge as ?! 0 to undercompressive shocks, in which the characteristics pass through the shock. The analysis is based on exp...

Construction and Qualitative Behavior of Solutions for a System of Nonlinear Hyperbolic Conservation Laws with Damping

Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...