Riemann problem for a non-strictly hyperbolic system in chemotaxis

A characteristic initial value problem for a strictly hyperbolic system

Consider the system Autt +Cuxx = f(x,t), (x,t) ∈ T for u(x,t) in R2, where A and C are real constant 2× 2 matrices, and f is a continuous function in R2. We assume that detC ≠ 0 and that the system is strictly hyperbolic in the sense that there are four distinct characteristic curves Γi, i= 1, . . . ,4, in xt-plane whose gradients (ξ1i,ξ2i) satisfy det[Aξ2 1i+ Cξ2 2i]= 0. We allow the character...

On the mixed problem for non strictly hyperbolic operators

The classical theory of strictly hyperbolic boundary value problems has received several extensions since the 70’s. One of the most noticeable is the result of Metivier establishing that Majda’s "block structure condition" for constantly hyperbolic operators, which implies well-posedness for the initial boundary value problem (IBVP) with zero initial data. The well-posedness of IBVP with non ze...

On the Riemann Problem for Non-conservative Hyperbolic Systems

Nvestigation of a Boundary Layer Problem for Perturbed Cauchy-Riemann Equation with Non-local Boundary Condition

Boundary layer problems (Singular perturbation problems) more have been applied for ordinary differential equations. While this theory for partial differential equations have many applications in several fields of physics and engineering. Because of complexity of limit and boundary behavior of the solutions of partial differential equations these problems considered less than ordinary case. In ...

Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem

Abstract. The Generalized Riemann Problem (GRP) for nonlinear hyperbolic system of m balance laws (or alternatively “quasi-conservative” laws) in one space dimension is formulated as follows: Given initial-data which are analytic on two sides of a discontinuity, determine the time evolution of the solution at the discontinuity. In particular, the GRP numerical scheme (second-order high resoluti...