Global secondary bifurcation in a non-linear boundary value problem

TY - JOUR

T1 - Global secondary bifurcation in a non-linear boundary value problem

AU - Davidson, F. A.

PY - 1999/12/1

Y1 - 1999/12/1

N2 - We consider a steady-state non-linear boundary value problem which arises in modelling the formation of vascular networks in response to tumour growth. Global bifurcation from both trivial and non-trivial solution branches is considered, with emphasis on the latter. By investigating such secondary bifurcation, it is shown that positive, bounded solutions exist for all physically relevant values of a critical parameter. A certain class of these solutions is discussed with respect to the application to tumour growth.

AB - We consider a steady-state non-linear boundary value problem which arises in modelling the formation of vascular networks in response to tumour growth. Global bifurcation from both trivial and non-trivial solution branches is considered, with emphasis on the latter. By investigating such secondary bifurcation, it is shown that positive, bounded solutions exist for all physically relevant values of a critical parameter. A certain class of these solutions is discussed with respect to the application to tumour growth.

U2 - 10.1006/jmaa.1999.6591

DO - 10.1006/jmaa.1999.6591

M3 - Article

SN - 0022-247X

VL - 240

SP - 80

EP - 91

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -