The Convergence of Successive Approximations for Boundary Value Problems of Hyperbolic Equations in the Banach Space
The linearization principle for some evolution problems arising in chemical kinetics.
The method of characteristics for hyperbolic boundary value problems on the plane.
The numerical interface coupling of nonlinear hyperbolic systems of conservation laws : II. The case of systems
We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem. We...
The numerical interface coupling of nonlinear hyperbolic systems of conservation laws: II. The case of systems
We study the theoretical and numerical coupling of two hyperbolic systems of conservation laws at a fixed interface. As already proven in the scalar case, the coupling preserves in a weak sense the continuity of the solution at the interface without imposing the overall conservativity of the coupled model. We develop a detailed analysis of the coupling in the linear case. In the nonlinear case, we either use a linearized approach or a coupling method based on the solution of a Riemann problem....
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Two phase flow arising in hydraulics
The aim of this paper is to proceed in the study of the system which will be specified below. The system concerns fluid flow in a simple hydraulic system consisting of a pipe with generator on one side and a valve or some more complicated hydraulic elements on the other end of the pipe. The purpose of the research is a rigorous mathematical analysis of the corresponding linearized system. Here, we analyze the linearized problem near the fixed steady state which already have been explicitly described....
Two-dimension Riemann initial-boundary value problem of scalar conservation laws with curved boundary.