## Abstract The author studies the mixed problem for the linear symmetric hyperbolic systems with maximally nonβnegative and characteristic boundary condition. Existence of a unique solution is proved inside a suitable class of functions of weighted Sobolev type which takes account of the loss of r
Symmetrization of Hyperbolic Systems with Non-degenerate Characteristics
β Scribed by T. Nishitani
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 728 KB
- Volume
- 132
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
β¦ Synopsis
We study symmetrization of hyperbolic first order systems. To be precise, generalizing non-degenerate double characteristics, we define non degenerate characteristics of any order. Then, assuming that the reference characteristic is non degenerate, we prove that the system is smoothly symmetrizable near the characteristic. Applying this result, we also show that non degenerate characteristics can not be removed by hyperbolic perturbations. 1995 Academic Press. Inc
π SIMILAR VOLUMES
We consider the initial-boundary value problem for quasi-linear symmetric hyperbolic systems with dissipation and characteristic boundary of constant multiplicity. We investigate the global existence and decay property of small regular solutions in suitable functions spaces which take into account t
We study some hyperbolic polycycles with two vertices which are degenerate and non-trivial and such that the maximal cyclicity in the sufficiently differentiable unfolding depends only on the vector field germ along the polycycle. In these cases, the maximal cyclicity and versal unfolding of the pol
## Abstract One often believes that there is no shock formation for the Cauchy problem of quasilinear hyperbolic systems (of conservation laws) with linearly degenerate characteristic fields. It has been a conjecture for a long time (see __Arch. Rational Mech. Anal.__ 2004; **172**:65β91; __Compres
## Abstract Following the abstract setting of [8] and using the global results of [2], global wellposedness and regularity results are proved for the solutions of quasiβlinear symmetric hyperbolic systems with bounded coefficients which are regularized by a convolution in the space variables with a