singular limit for relaxation and viscosity approximations of extended traffic flow models.
stability of conservation laws for a traffic flow model.
-type contraction for systems of conservation laws
The semi-group associated with the Cauchy problem for a scalar conservation law is known to be a contraction in . However it is not a contraction in for any . Leger showed in [20] that for a convex flux, it is however a contraction in up to a suitable shift. We investigate in this paper whether such a contraction may happen for systems. The method is based on the relative entropy method. Our general analysis leads us to the new geometrical notion of Genuinely non-Temple systems. We treat in...
well-posed Cauchy problems and symmetrizability of first order systems
The Cauchy problem for first order system is known to be well-posed in when it admits a microlocal symmetrizer which is smooth in and Lipschitz continuous in . This paper contains three main results. First we show that a Lipschitz smoothness globally in is sufficient. Second, we show that the existence of symmetrizers with a given smoothness is equivalent to the existence of full symmetrizers having the same smoothness. This notion was first introduced in [FL67]. This is the key point...
-regularity of the boundary to boundary operator for hyperbolic and Petrowski PDEs.
weighted estimate for the wave equation with potential
We consider a potential type perturbation of the three dimensional wave equation and we establish a dispersive estimate for the associated propagator. The main estimate is proved under the assumption that the potential satisfies where .
-decay of solutions to dissipative-dispersive perturbations of conservation laws
We study the decay in time of the spatial -norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.
-estimates for hyperbolic operators applications to
estimates for the wave equation and applications
--Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
We prove the --time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the --time decay estimates.
-oценки решений задачи Коши для одномерного гиперболического уравнения
-oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами
-regularity of solutions to first initial-boundary value problem for hyperbolic equations in cusp domains.
-оценки решения смешанной задачи с условиями Дирихле для волнового уравнения при радиальных начальных данных
estimates for damped wave equations with odd initial data.
L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods
We prove stability and derive error estimates for the recently introduced central discontinuous Galerkin method, in the context of linear hyperbolic equations with possibly discontinuous solutions. A comparison between the central discontinuous Galerkin method and the regular discontinuous Galerkin method in this context is also made. Numerical experiments are provided to validate the quantitative conclusions from the analysis.
La condition nulle pour les équations hyperboliques en dimension deux d’espace
Laplace transform pairs of N-dimensions and second order linear partial differential equations with constant coefficients.
Large diffusivity finite-dimensional asymptotic behaviour of a semilinear wave equation.
Large energy simple modes for a class of Kirchhoff equations.