Details
| Original language | English |
|---|---|
| Pages (from-to) | 1-20 |
| Number of pages | 20 |
| Journal | Nonlinear Differential Equations and Applications |
| Volume | 17 |
| Issue number | 1 |
| Publication status | Published - 2 Oct 2009 |
Abstract
The growth of tumors is an important subject in recent research. We present here a mathematical model for the growth of nonnecrotic tumors in all the three regimes of vascularisation. This leads to a free-boundary problem which we treat by means ODE techniques. We prove the existence of a unique radially symmetric stationary solution. It is also shown that, if the initial tumor is radially symmetric, there exists a unique radially symmetric solution of the evolution equation, which exists for all times. The asymptotic behaviour of this solution will be discussed in relation to the parameters characterizing cell proliferation and cell death.
Keywords
- Free boundary problem, Radial symmetry, Tumor growth
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Nonlinear Differential Equations and Applications, Vol. 17, No. 1, 02.10.2009, p. 1-20.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Radially symmetric growth of nonnecrotic tumors
AU - Escher, Joachim
AU - Matioc, Anca Voichita
PY - 2009/10/2
Y1 - 2009/10/2
N2 - The growth of tumors is an important subject in recent research. We present here a mathematical model for the growth of nonnecrotic tumors in all the three regimes of vascularisation. This leads to a free-boundary problem which we treat by means ODE techniques. We prove the existence of a unique radially symmetric stationary solution. It is also shown that, if the initial tumor is radially symmetric, there exists a unique radially symmetric solution of the evolution equation, which exists for all times. The asymptotic behaviour of this solution will be discussed in relation to the parameters characterizing cell proliferation and cell death.
AB - The growth of tumors is an important subject in recent research. We present here a mathematical model for the growth of nonnecrotic tumors in all the three regimes of vascularisation. This leads to a free-boundary problem which we treat by means ODE techniques. We prove the existence of a unique radially symmetric stationary solution. It is also shown that, if the initial tumor is radially symmetric, there exists a unique radially symmetric solution of the evolution equation, which exists for all times. The asymptotic behaviour of this solution will be discussed in relation to the parameters characterizing cell proliferation and cell death.
KW - Free boundary problem
KW - Radial symmetry
KW - Tumor growth
UR - http://www.scopus.com/inward/record.url?scp=76949089140&partnerID=8YFLogxK
U2 - 10.1007/s00030-009-0037-6
DO - 10.1007/s00030-009-0037-6
M3 - Article
AN - SCOPUS:76949089140
VL - 17
SP - 1
EP - 20
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
SN - 1021-9722
IS - 1
ER -