Details
| Original language | English |
|---|---|
| Pages (from-to) | 573-596 |
| Number of pages | 24 |
| Journal | Discrete and Continuous Dynamical Systems - Series B |
| Volume | 15 |
| Issue number | 3 |
| Publication status | Published - 1 May 2011 |
Abstract
We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain and one for the pressure inside the tumor. These variables are coupled by a relation which describes the dynamic of the boundary. By re-expressing the problem as an abstract evolution equation, we prove local well-posedness in the small Hölder spaces context. Further on, we use the principle of linearised stability to characterise the stability properties of the unique radially symmetric equilibrium of the problem.
Keywords
- Moving boundary problem, Stability, Tumor growth, Well-posedness
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Discrete and Continuous Dynamical Systems - Series B, Vol. 15, No. 3, 01.05.2011, p. 573-596.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Well-posedness and stability analysis for a moving boundary problem modelling the growth of nonnecrotic tumors
AU - Escher, Joachim
AU - Matioc, Anca Voichita
PY - 2011/5/1
Y1 - 2011/5/1
N2 - We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain and one for the pressure inside the tumor. These variables are coupled by a relation which describes the dynamic of the boundary. By re-expressing the problem as an abstract evolution equation, we prove local well-posedness in the small Hölder spaces context. Further on, we use the principle of linearised stability to characterise the stability properties of the unique radially symmetric equilibrium of the problem.
AB - We study a moving boundary problem describing the growth of nonnecrotic tumors in different regimes of vascularisation. This model consists of two decoupled Dirichlet problem, one for the rate at which nutrient is added to the tumor domain and one for the pressure inside the tumor. These variables are coupled by a relation which describes the dynamic of the boundary. By re-expressing the problem as an abstract evolution equation, we prove local well-posedness in the small Hölder spaces context. Further on, we use the principle of linearised stability to characterise the stability properties of the unique radially symmetric equilibrium of the problem.
KW - Moving boundary problem
KW - Stability
KW - Tumor growth
KW - Well-posedness
UR - http://www.scopus.com/inward/record.url?scp=79954459447&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2011.15.573
DO - 10.3934/dcdsb.2011.15.573
M3 - Article
AN - SCOPUS:79954459447
VL - 15
SP - 573
EP - 596
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 3
ER -