This book provides a self-contained introduction to the mathematical theory of hyperbolic
systems of conservation laws, with particular emphasis on the study of discontinuous …

We introduce a new homogenized hyperbolic (multiclass) traffic flow model, which allows us
to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.) and …

We give examples of finite time blowup in sup-norm and total variation for 3× 3-systems of
strictly hyperbolic conservation laws. The exact solutions are explicitly constructed. In the …

Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear,
Temple class system of conservation laws eq: 1 u_t+ f (u) _x= 0,\qquad u (0, x)=\ov u …

We study the behavior of the Aw–Rascle–Zhang model when the relaxation parameter
converges to zero. In a Lagrangian setting, we use the wavefront tracking method with …

We obtain various new well-posedness results for continuity and transport equations, among
them an existence and uniqueness theorem (in the class of strongly continuous solutions) in …

One-dimensional hyperbolic conservation laws: Past and future Page 1 December 13, 2024
16:21 WSPC/S0219-8916 JHDE 2440002 Journal of Hyperbolic Differential Equations Vol. 21 …

We prove that the Riemann solutions are stable for the chromatography system under the
local small perturbations of the Riemann initial data. The proof is based on the detailed …

The paper discusses various regularity properties for solutions to a scalar, 1-dimensional
conservation law with strictly convex flux and integrable source. In turn, these yield …

We consider a hyperbolic system of conservation laws \left{u_t+f(u)_x=0,\u(0,⋅)=u_0,. where
each characteristic field is either linearly degenerate or genuinely nonlinear. Under the …