Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlocal solutions of parabolic equations with strongly elliptic
  differential operators   The paper deals with second order parabolic equations on bounded domains with
Dirichlet conditions in arbitrary Euclidean spaces. Their interest comes from
being models for describing reaction-diffusion processes in several frameworks.
A linear diffusion term in divergence form is included which generates a
strongly elliptic differential operator. A further linear part, of integral
type, is present which accounts of nonlocal diffusion behaviours. The main
result provides a unifying method for studying the existence and localization
of solutions satisfying nonlocal associated boundary conditions. The Cauchy
multipoint and the mean value conditions are included in this investigation.
The problem is transformed into its abstract setting and the proofs are based
on the homotopic invariance of the Leray-Schauder topological degree. A
bounding function (i.e. Lyapunov-like function) theory is developed, which is
new in this infinite dimensional context. It allows that the associated vector
fields have no fixed points on the boundary of their domains and then it makes
possible the use of a degree argument.

15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc