Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak* solutions I: A new perspective on solutions to systems of
  conservation laws   We introduce a new notion of solution, which we call weak* solutions, for
systems of conservation laws. These solutions can be used to handle singular
situations that standard weak solutions cannot, such as vacuums in Lagrangian
gas dynamics or cavities in elasticity. Our framework allows us to treat the
systems as ODEs in Banach space. Starting with the observation that solutions
act linearly on test functions $\alpha\in X$, we require solutions to take
values in the dual space $X^*$ of $X$. Moreover, we weaken the usual
requirement of measurability of solutions. In order to do this, we develop the
calculus of the Gelfand integral, which is appropriate for weak* measurable
functions. We then use the Gelfand calculus to define weak* solutions, and show
that they are stronger than the usual notion of weak solution, although for
$BV$ solutions the notions are equivalent. It is expected that these solutions
will also shed light on vexing issues of ill-posedness for multi-dimensional
systems.

26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th