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$L^{1}$ stability of conservation laws for a traffic flow model.

Li, Tong (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

$L^{2}$ well-posed Cauchy problems and symmetrizability of first order systems

Guy Métivier (2014)

Journal de l’École polytechnique — Mathématiques

The Cauchy problem for first order system $L (t, x, \partial_{t}, \partial_{x})$ is known to be well-posed in $L^{2}$ when it admits a microlocal symmetrizer $S (t, x, ξ)$ which is smooth in $ξ$ and Lipschitz continuous in $(t, x)$ . This paper contains three main results. First we show that a Lipschitz smoothness globally in $(t, x, ξ)$ 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...

$L^{p}$ - $L^{q}$ -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

We prove the $L^{p}$ - $L^{q}$ -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 $L^{p}$ - $L^{q}$ -time decay estimates.

L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

Yingjie Liu, Chi-Wang Shu, Eitan Tadmor, Mengping Zhang (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

 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.

We prove the local in time existence of solutions for an aggregation equation in Besov spaces. The Fourier localization technique and Littlewood-Paley theory are the main tools used in the proof.

Displaying 1 – 8 of 8

$L^{1}$ stability of conservation laws for a traffic flow model.

$L^{2}$ well-posed Cauchy problems and symmetrizability of first order systems

$L^{p}$ - $L^{q}$ -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

L2 stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods

Large Time Behavior of Solutions of Hyperbolic Balance laws

Le problème de Cauchy et la propagation des singularités pour une classe des systèmes hyperboliques non symétrisables

Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow.

Local existence of solutions for an aggregation equation in Besov spaces

Currently displaying 1 – 8 of 8