A locally contractive metric for systems of conservation laws
A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells.
A Matrix Approach to the Energy-Norm Bisection in Wave Motion
A maximum principle for optimally controlled systems of conservation laws
A memory type boundary stabilization of a mildly damped wave equation.
A Method of Characteristics Solving the Initial-Boundary Value Problem of a Hyperbolic Differential Equation of Second Order.
A microscopic model for the Burgers equation and longest increasing subsequences.
A mixed problem for a hyperbolic system on the plane with delay in the boundary conditions.
A mixed problem for quasilinear impulsive hyperbolic equations with non stationary boundary and transmission conditions.
A mixed problem with only integral boundary conditions for a hyperbolic equation.
A model for dip-coating of a two liquid mixture.
A model for passive damping of a membrane
A monotonicity method for solving hyperbolic problems with hysteresis
A mountain pass method for the numerical solution of semilinear wave equations.
A multidimensional analogue of the Denjoy-Perron-Henstock-Kurzweil integral.
A Multiscale Model Reduction Method for Partial Differential Equations
We propose a multiscale model reduction method for partial differential equations. The main purpose of this method is to derive an effective equation for multiscale problems without scale separation. An essential ingredient of our method is to decompose the harmonic coordinates into a smooth part and a highly oscillatory part so that the smooth part is invertible and the highly oscillatory part is small. Such a decomposition plays a key role in our construction of the effective equation. We show...
A “natural” norm for the method of characteristics using discontinuous finite elements : 2D and 3D case
A “Natural” Norm for the Method of Characteristics Using Discontinuous Finite Elements : 2D and 3D case
We consider the numerical approximation of a first order stationary hyperbolic equation by the method of characteristics with pseudo time step k using discontinuous finite elements on a mesh . For this method, we exhibit a “natural” norm || ||h,k for which we show that the discrete variational problem is well posed and we obtain an error estimate. We show that when k goes to zero problem (resp. the || ||h,k norm) has as a limit problem (Ph) (resp. the || ||h norm) associated to the...
A necessary and sufficient condition for the diagonalization of multi-dimensional quasilinear systems.
A necessary and sufficient condition for the existence of an exponential attractor
We give a necessary and sufficient condition for the existence of an exponential attractor. The condition is formulated in the context of metric spaces. It also captures the quantitative properties of the attractor, i.e., the dimension and the rate of attraction. As an application, we show that the evolution operator for the wave equation with nonlinear damping has an exponential attractor.