About the existence and uniqueness theorem for hyperbolic equation.
About the influence of oscillations on Strichartz-type decay estimates.
Abstract linear hyperbolic equations and asymptotic equivalence as
Abstract semilinear equations with small nonlinearities
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Accurate numerical discretizations of non-conservative hyperbolic systems
We present an alternative framework for designing efficient numerical schemes for non-conservative hyperbolic systems. This approach is based on the design of entropy conservative discretizations and suitable numerical diffusion operators that mimic the effect of underlying viscous mechanisms. This approach is illustrated by considering two model non-conservative systems: Lagrangian gas dynamics in non-conservative form and a form of isothermal Euler equations. Numerical experiments demonstrating...
Adaptive data distribution for concurrent continuation.
Adaptive fast marching and level set methods for propagating interfaces.
Adaptive finite element relaxation schemes for hyperbolic conservation laws
We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...
Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws
We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...
Adaptive mesh refinement strategy for a non conservative transport problem
Long time simulations of transport equations raise computational challenges since they require both a large domain of calculation and sufficient accuracy. It is therefore advantageous, in terms of computational costs, to use a time varying adaptive mesh, with small cells in the region of interest and coarser cells where the solution is smooth. Biological models involving cell dynamics fall for instance within this framework and are often non conservative to account for cell division. In that case...
Adaptive multiscale scheme based on numerical density of entropy production for conservation laws
We propose a 1D adaptive numerical scheme for hyperbolic conservation laws based on the numerical density of entropy production (the amount of violation of the theoretical entropy inequality). This density is used as an a posteriori error which provides information if the mesh should be refined in the regions where discontinuities occur or coarsened in the regions where the solution remains smooth. As due to the Courant-Friedrich-Levy stability condition the time step is restricted and leads to...
Adaptive parameter estimation of hyperbolic distributed parameter systems : non-symmetric damping and slowly time varying systems
Adaptive Parameter Estimation of Hyperbolic Distributed Parameter Systems: Non-symmetric Damping and Slowly Time Varying Systems
In this paper a model reference-based adaptive parameter estimator for a wide class of hyperbolic distributed parameter systems is considered. The proposed state and parameter estimator can handle hyperbolic systems in which the damping sesquilinear form may not be symmetric (or even present) and a modification to the standard adaptive law is introduced to account for this lack of symmetry (or absence) in the damping form. In addition, the proposed scheme is modified for systems in which the input...
Addendum à «R. G. McLenaghan : on the validity of Huygens' principle for second order partial differential equations with four independent variables. I»
Addition to the Fichera paper
Air entrainment in transient flows in closed water pipes : A two-layer approach
In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme...
Almost global solutions for non hamiltonian semi-linear Klein-Gordon equations on compact revolution hypersurfaces
This paper is devoted to the proof of almost global existence results for Klein-Gordon equations on compact revolution hypersurfaces with non-Hamiltonian nonlinearities, when the data are smooth, small and radial. The method combines normal forms with the fact that the eigenvalues associated to radial eigenfunctions of the Laplacian on such manifolds are simple and satisfy convenient asymptotic expansions.
Almost periodic solutions of nonlinear hyperbolic equations with time delay.
Almost product structures and Monge-Ampère equations.