Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spikes and diffusion waves in one-dimensional model of chemotaxis   We consider the one-dimensional initial value problem for the viscous
transport equation with nonlocal velocity $u_t = u_{xx} - \left(u (K^\prime
\ast u)\right)_{x}$ with a given kernel $K'\in L^1(\R)$. We show the existence
of global-in-time nonnegative solutions and we study their large time
asymptotics. Depending on $K'$, we obtain either linear diffusion waves ({\it
i.e.}~the fundamental solution of the heat equation) or nonlinear diffusion
waves (the fundamental solution of the viscous Burgers equation) in asymptotic
expansions of solutions as $t\to\infty$. Moreover, for certain aggregation
kernels, we show a concentration of solution on an initial time interval, which
resemble a phenomenon of the spike creation, typical in chemotaxis models.

8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom