Details
| Original language | English |
|---|---|
| Pages (from-to) | 210-235 |
| Number of pages | 26 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 39 |
| Issue number | 1 |
| Publication status | Published - 2007 |
Abstract
We study bifurcations from radially symmetric solutions of a free boundary problem modelling the dormant state of nonnecrotic avascular tumors. This problem consists of two semilinear elliptic equations with a Dirichlet and a Neumann boundary condition, respectively, and a third boundary condition coupling surface tension effects on the free interface to the internal pressure. By reducing the full problem to an abstract bifurcation equation in terms of the free boundary only and by characterizing the linearization as a Fourier multiplication operator, we carry out a precise analysis of local bifurcations of this problem.
Keywords
- Bifurcation, Elliptic equations, Free boundary problem, Surface tension, Tumor growth
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Mathematical Analysis, Vol. 39, No. 1, 2007, p. 210-235.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Bifurcation analysis of an elliptic free boundary problem modelling the growth of avascular tumors
AU - Cui, Shangbin
AU - Escher, Joachim
PY - 2007
Y1 - 2007
N2 - We study bifurcations from radially symmetric solutions of a free boundary problem modelling the dormant state of nonnecrotic avascular tumors. This problem consists of two semilinear elliptic equations with a Dirichlet and a Neumann boundary condition, respectively, and a third boundary condition coupling surface tension effects on the free interface to the internal pressure. By reducing the full problem to an abstract bifurcation equation in terms of the free boundary only and by characterizing the linearization as a Fourier multiplication operator, we carry out a precise analysis of local bifurcations of this problem.
AB - We study bifurcations from radially symmetric solutions of a free boundary problem modelling the dormant state of nonnecrotic avascular tumors. This problem consists of two semilinear elliptic equations with a Dirichlet and a Neumann boundary condition, respectively, and a third boundary condition coupling surface tension effects on the free interface to the internal pressure. By reducing the full problem to an abstract bifurcation equation in terms of the free boundary only and by characterizing the linearization as a Fourier multiplication operator, we carry out a precise analysis of local bifurcations of this problem.
KW - Bifurcation
KW - Elliptic equations
KW - Free boundary problem
KW - Surface tension
KW - Tumor growth
UR - http://www.scopus.com/inward/record.url?scp=39449127707&partnerID=8YFLogxK
U2 - 10.1137/060657509
DO - 10.1137/060657509
M3 - Article
AN - SCOPUS:39449127707
VL - 39
SP - 210
EP - 235
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
SN - 0036-1410
IS - 1
ER -