Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A locally quadratic Glimm functional and sharp convergence rate of the
  Glimm scheme for nonlinear hyperbolic systems   Consider the Cauchy problem for a strictly hyperbolic, $N\times N$
quasilinear system in one space dimension $$ u_t+A(u) u_x=0,\qquad u(0,x)=\bar
u(x), \eqno (1) $$ where $u \mapsto A(u)$ is a smooth matrix-valued map, and
the initial data $\overline u$ is assumed to have small total variation. We
investigate the rate of convergence of approximate solutions of (1) constructed
by the Glimm scheme, under the assumption that, letting $\lambda_k(u)$,
$r_k(u)$ denote the $k$-th eigenvalue and a corresponding eigenvector of
$A(u)$, respectively, for each $k$-th characteristic family the linearly
degenerate manifold $$
  \mathcal{M}_k \doteq \big\{u\in\Omega : \nabla\lambda_k(u)\cdot
r_k(u)=0\big\} $$ is either the whole space, or it is empty, or it consists of
a finite number of smooth, $N-1$-dimensional, connected, manifolds that are
transversal to the characteristic vector field $r_k$. We introduce a Glimm type
functional which is the sum of the cubic interaction potential defined in
\cite{sie}, and of a quadratic term that takes into account interactions of
waves of the same family with strength smaller than some fixed threshold
parameter. Relying on an adapted wave tracing method, and on the decrease
amount of such a functional, we obtain the same type of error estimates valid
for Glimm approximate solutions of hyperbolic systems satisfying the classical
Lax assumptions of genuine nonlinearity or linear degeneracy of the
characteristic families.

22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess