Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp interface limit of a diffuse interface model for tumor-growth   We consider the asymptotic limit of a diffuse interface model for
tumor-growth when a parameter $\varepsilon$ proportional to the thickness of
the diffuse interface goes to zero. An approximate solution which shows
explicitly the behavior of the true solution for small $\varepsilon$ will be
constructed by using matched expansion method. Based on the energy method, a
spectral condition in particular, we establish a smallness estimate of the
difference between the approximate solution and the true solution.

4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th