Details
| Original language | English |
|---|---|
| Pages (from-to) | 173-193 |
| Number of pages | 21 |
| Journal | Archive for Rational Mechanics and Analysis |
| Volume | 191 |
| Issue number | 1 |
| Publication status | Published - Jan 2009 |
Abstract
We study a moving boundary problem modeling the growth of in vitro tumors. This problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure, respectively, and a first-order partial differential equation describing the evolution of the moving boundary. An important feature is that the effect of surface tension on the moving boundary is taken into account. We show that this problem is locally well-posed for a large class of initial data by using analytic semi-group theory. We also prove that if the surface tension coefficient γ is larger than a threshold value γ * then the unique flat equilibrium is asymptotically stable, whereas in the case γ < γ * this flat equilibrium is unstable.
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Mathematics (miscellaneous)
- Engineering(all)
- Mechanical Engineering
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Archive for Rational Mechanics and Analysis, Vol. 191, No. 1, 01.2009, p. 173-193.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Well-posedness and Stability of a Multi-dimensional Tumor Growth Model
AU - Cui, Shangbin
AU - Escher, Joachim
PY - 2009/1
Y1 - 2009/1
N2 - We study a moving boundary problem modeling the growth of in vitro tumors. This problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure, respectively, and a first-order partial differential equation describing the evolution of the moving boundary. An important feature is that the effect of surface tension on the moving boundary is taken into account. We show that this problem is locally well-posed for a large class of initial data by using analytic semi-group theory. We also prove that if the surface tension coefficient γ is larger than a threshold value γ * then the unique flat equilibrium is asymptotically stable, whereas in the case γ < γ * this flat equilibrium is unstable.
AB - We study a moving boundary problem modeling the growth of in vitro tumors. This problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure, respectively, and a first-order partial differential equation describing the evolution of the moving boundary. An important feature is that the effect of surface tension on the moving boundary is taken into account. We show that this problem is locally well-posed for a large class of initial data by using analytic semi-group theory. We also prove that if the surface tension coefficient γ is larger than a threshold value γ * then the unique flat equilibrium is asymptotically stable, whereas in the case γ < γ * this flat equilibrium is unstable.
UR - http://www.scopus.com/inward/record.url?scp=55849128464&partnerID=8YFLogxK
U2 - 10.1007/s00205-008-0158-9
DO - 10.1007/s00205-008-0158-9
M3 - Article
AN - SCOPUS:55849128464
VL - 191
SP - 173
EP - 193
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
SN - 0003-9527
IS - 1
ER -