A nonconvex scalar conservation law with trilinear flux

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...

On the Attainable Set for a Scalar Nonconvex Conservation Law

We consider a Cauchy problem for a scalar conservation law in one space dimension with a compactly supported initial datum,

A Scalar Conservation Law with Discontinuous Flux for Supply Chains with Finite Buffers

An aggregate continuum model for production flows and supply chains with finite buffers is proposed and analyzed. The model extends earlier partial differential equations that represent deterministic coarse grained models of stochastic production systems based on mass conservation. The finite size buffers lead to a discontinuous clearing function describing the throughput as a function of the w...

Zero Diffusion-Dispersion-Smoothing Limits for a Scalar Conservation Law with Discontinuous Flux Function

New Entropy Conditions for the Scalar Conservation Law with Discontinuous Flux

We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux in rather general form (no convexity or genuine linearity is needed). We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely under the assumption that initial data belong to the BVclass. Such initial data enable us to...