Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of a new multispecies tumor growth model coupling 3D
  phase-fields with a 1D vascular network   In this work, we present and analyze a mathematical model for tumor growth
incorporating ECM erosion, interstitial flow, and the effect of vascular flow
and nutrient transport. The model is of phase-field or diffused-interface type
in which multiple phases of cell species and other constituents are separated
by smooth evolving interfaces. The model involves a mesoscale version of
Darcy's law to capture the flow mechanism in the tissue matrix. Modeling flow
and transport processes in the vasculature supplying the healthy and cancerous
tissue, one-dimensional (1D) equations are considered. Since the models
governing the transport and flow processes are defined together with cell
species models on a three-dimensional (3D) domain, we obtain a 3D-1D coupled
model. We show some mathematical results on the existence of weak solutions.
Furthermore, simulation results are presented illustrating the evolution of
tumors and the effects of ECM erosion.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th