2 papers
math.NA2024
A Shape-Newton Method for Free-boundary Problems Subject to The Bernoulli Boundary Condition
Yiyun Fan, John Billingham, Kristoffer van der Zee
We develop a shape-Newton method for solving generic free-boundary problems where one of the free-boundary conditions is governed by the Bernoulli equation. The Newton-like scheme…
math.AP2024
The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line
D. J. Needham, J. Billingham, N. M. Ladas +1
We study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \[ u_t = D u_{xx} + u(1-Ï*u), \] where is a spatial convolution…