Global Weak Entropy Solution of Nonlinear Ideal Reaction Chromatography System and Applications

The ideal reaction chromatography model can be regarded as a semi-coupled system of two hyperbolic partial differential equations, in which, one is a self-closed nonlinear equation for the reactant concentration and another is a linear equation coupling the reactant concentration for the resultant concentration. This paper is concerned with the initial-boundary value problem for the above model. By the characteristic method and the truncation method, we construct the global weak entropy solution of this initial initial-boundary value problem for Riemann type of initial-boundary data. Moreover, as examples, we apply the obtained results to the cases of head-on and wide pulse injections and give the expression of the global weak entropy solution.

Generalized Persistence of Entropy Weak Solutions for System of Hyperbolic Conservation Laws

Let u(t,x)be the solution to the Cauchy problem of a scalar conservation law in one space dimension.It is well known that even for smooth initial data the solution can become discontinuous in finite time and global entropy weak solution can best lie in the space of bounded total variations.It is impossible that the solutions belong to,for example,H^(1) because by Sobolev embedding theorem H^(1) functions are Holder continuous.However,the author notes that from any point(t,x),he can draw a generalized characteristic downward which meets the initial axis at y=α(t,x).If he regards u as a function of(t,y),it indeed belongs to H^(1) as a function of y if the initial data belongs to H^(1).He may call this generalized persistence(of high regularity)of the entropy weak solutions.The main purpose of this paper is to prove some kinds of generalized persistence(of high regularity)for the scalar and 2×2 Temple system of hyperbolic conservation laws in one space dimension.

ON THE CAUCHY PROBLEM FOR AW-RASCLE SYSTEM WITH LINEAR DAMPING

The existence of global BV solutions for the Aw-Rascle system with linear damping is considered.In order to get approximate solutions we consider the system in Lagrangian coordinates,then by using the wave front tracking method coupling with and suitable splitting algorithm and the ideas of[1]we get a sequence of approximate solutions.Finally we show the convergence of this approximate sequence to the weak entropic solution.

Construction of Solutions and L^1-error Estimates of Viscous Methods for Scalar Conservation Laws with Boundary

This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type： an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L^1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O（ε^1/2） in L^1-norm; otherwise, as in the initial value problem, the L^1-error bound is O（ε｜ In ε｜）.