On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients

The Cauchy Problem for Wave Equations with non Lipschitz Coefficients

In this paper we study the Cauchy problem for second order strictly hyperbolic operators of the form

Precise Finite Speed and Uniqueness in the Cauchy Problem for Symmetrizable Hyperbolic Systems

Precise finite speed, in the sense of that the domain of influence is a subset of the union of influence curves through the support of the initial data is proved for hyperbolic systems symmetrized by pseudodifferential operators in the spatial variables. From this, uniqueness in the Cauchy problem at spacelike hypersurfaces is derived by a Hölmgren style duality argument. Sharp finite speed is ...

On the Cauchy Problem for Nonlinear Hyperbolic Systems

This paper consider various examples of metrics which are contractive w.r.t. an evolution semigroup, and discusses the possibility of an abstract O.D.E. theory on metric spaces, with applications to hyperbolic systems. In particular, using a recently introduced deenition of Viscosity Solutions, it is shown how a strictly hyperbolic system of conservation laws can be reformulated as an abstract ...

The Cauchy Problem for Wave Equations with Non Lipschitz Coefficients; Application to Continuation of Solutions of Some Nonlinear Wave Equations

Discontinuous Galerkin error estimation for linear symmetrizable hyperbolic systems

We present an a posteriori error analysis for the discontinuous Galerkin discretization error of first-order linear symmetrizable hyperbolic systems of partial differential equations with smooth solutions. We perform a local error analysis by writing the local error as a series and showing that its leading term can be expressed as a linear combination of Legendre polynomials of degree p and p +...