A property of the defining equations for the Lie algebra in the group classification problem for wave equations.
A remark on global smooth solutions for quasilinear wave equations
A remark on the blow-up of the solutions of a partial differential equation.
A result of existence for an original convection-diffusion equation.
En este artículo se estudia el análisis matemático de una ley de conservación que no es clásica. El modelo describe procesos estatigráficos en Geología y tiene en cuenta una condición de tasa de erosión limitada. En primer lugar se presentan el modelo físico y la formulación matemática (posiblemente nueva). Tras enunciar la definición solución se presentan las herramientas que permiten probar la existencia de soluciones.
A result on the well posedness of the Cauchy problem for a class of hyperbolic operators with double characteristics
A Riemann problem with small viscosity and dispersion.
A Riemann restricted characterization of the quasilinearity hierarchy: some remarks.
A robust entropy−satisfying finite volume scheme for the isentropic Baer−Nunziato model
We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions. The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing...
A scaled characteristics method for the asymptotic solution of weakly nonlinear wave equations.
A selfadjoint hyperbolic boundary-value problem.
A self-adjoint “simultaneous crossing of the axis”.
A sharp Strichartz estimate for the wave equation with data in the energy space
We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the norm of the solution in terms of the energy. We also characterise the maximisers.
A shock-capturing discontinuous Galerkin method for the numerical solution of inviscid compressible flow
A simple construction of a parametrix for a regular hyperbolic operator
A Simple Example of Localized Parametric Resonance for the Wave Equation
2000 Mathematics Subject Classification: 35L05, 35P25, 47A40.The problem studied here was suggested to us by V. Petkov. Since the beginning of our careers, we have benefitted from his insights in partial differential equations and mathematical physics. In his writings and many discussions, the conjuction of deep analysis and specially interesting problems has been a source inspiration for us.The research of J. Rauch is partially supported by the U.S. National Science Foundation under grant NSF-DMS-0104096...
A singular controllability problem with vanishing viscosity
The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? The characteristic of our viscous term is that it contains the fractional power α of the Dirichlet Laplace operator. Through the parameter α we may increase or decrease the strength of the high frequencies damping which allows us to cover a large class of dissipative mechanisms. The viscous term,...
A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system where . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the norm.
A Sobolev-type inequality with applications.
A stability estimate for a solution in the inverse problem of finding the coefficients of lower derivatives.
A stability estimate for a solution of the problem of determining the dielectric permittivity.