A Canonical Form of a System of Microdifferential Equations with Non-Involutory Characteristics and Branching of Singularities.
A Convergent Finite Elemet Formulation for Transonic Flow.
A Glimm type functional for a special Jin–Xin relaxation model
A hybrid semi-primitive shock capturing scheme for conservation laws.
A locally contractive metric for systems of conservation laws
A note on critical times of quasilinear hyperbolic systems
In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.
A note on poroacoustic traveling waves under Darcy's law: Exact solutions
A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...
A shock-capturing discontinuous Galerkin method for the numerical solution of inviscid compressible flow
A Sobolev-type inequality with applications.
A three-point boundary-value problem for a hyperbolic equation with a non-local condition.
An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics
Asymptotic behavior for the centered-rarefaction appearance problem.
Boundary layers in weak solutions of hyperbolic conservation laws. III: Vanishing relaxation limits.
Colombeau's theory and shock wave solutions for systems of PDEs.
Conormalité des ondes semi-linéaires le long des caustiques
Control of transonic shock positions
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
Control of Transonic Shock Positions
We wish to show how the shock position in a nozzle could be controlled. Optimal control theory and algorithm is applied to the transonic equation. The difficulty is that the derivative with respect to the shock position involves a Dirac mass. The one dimensional case is solved, the two dimensional one is analyzed .
Description of the multi-dimensional finite volume solver EULER
This paper is aimed at the description of the multi-dimensional finite volume solver EULER, which has been developed for the numerical solution of the compressible Euler equations during several last years. The present overview of numerical schemes and the explanation of numerical techniques and tricks which have been used for EULER could be of certain interest not only for registered users but also for numerical mathematicians who have decided to implement a finite volume solver themselves. This...
Development of singularities in solutions of a hyperbolic system.
Diffraction des singularités analytiques dans les problèmes aux limites de la physique mathématique par les méthodes de Kawai-Kashiwara et Sjöstrand