Hyperbolic conservation laws on manifolds with limited regularity
نویسندگان
چکیده
منابع مشابه
Hyperbolic conservation laws on manifolds with limited regularity
We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the important case of Lorentzian manifolds. Only limited regularity is assumed on the geometry of the manifold. For this problem, we establish the existence and uniquene...
متن کاملHyperbolic conservation laws and spacetimes with limited regularity
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows andgeneral relativity. Recentworkby the author and his collaborators attempts to set the foundations for a study of weak solutions defined on Riemannian or Lorentzian manifolds and includes an investigation of the existence and qualitative behavior of solutions. The metric on the manifold may either ...
متن کاملLecture Notes on Hyperbolic Conservation Laws
These notes provide an introduction to the theory of hyperbolic systems of conservation laws in one space dimension. The various chapters cover the following topics: 1. Meaning of the conservation equations and definition of weak solutions. 2. Shocks, Rankine-Hugoniot equations and admissibility conditions. 3. Genuinely nonlinear and linearly degenerate characteristic fields. Solution to the Ri...
متن کاملOn Sobolev Regularizations of Hyperbolic Conservation Laws
1. INTRODUCI7ON We study certain Sobolev-type regularizations of the hyperbolic conservation laws that add terms simulating both dissipative and dispersive processes. These evolution equations have the form with the auxiliary specification The behaviour in L'(R) of the solutions of problem (S), as well as the value of (S) as an approximation to problem (C), is studied. Convergence results, with...
متن کاملOn Elementary Interactions for Hyperbolic Conservation Laws
This is a survey of interactions of weak nonlinear waves in N × N systems of hyperbolic conservation laws. Recently a variety of surprising new phenomena have been observed, including strong nonlinear instability of solutions. This implies that further assumptions must be made to develop a Glimm–Lax existence and decay theory for N ≥ 3. As a first step towards such a theory, a systematic descri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2008
ISSN: 1631-073X
DOI: 10.1016/j.crma.2008.03.017