5 papers
A tractable mathematical model for tissue growth
Joe Eyles, John F. King, Vanessa Styles
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological…
Type II Singularities on complete non-compact Yamabe flow
Beomjun Choi, Panagiota Daskalopoulos, John King
This work concerns with the existence and detailed asymptotic analysis of Type II singularities for solutions to complete non-compact conformally flat Yamabe flow with cylindrical…
New type I ancient compact solutions of the Yamabe flow
Panagiota Daskalopoulos, Manuel del Pino, John King +1
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as , to two self-similar complete non-compact s…
Type I ancient compact solutions of the Yamabe flow
Panagiota Daskalopoulos, Manuel del Pino, John King +1
We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as , to two self-similar complete non-compact s…
Extinction profile of complete non-compact solutions to the Yamabe flow
Panagiota Daskalopoulos, John King, Natasa Sesum
This work addresses the {\em singularity formation} of complete non-compact solutions to the conformally flat Yamabe flow whose conformal factors have {\em cylindrical behavior at…