4 papers
Well-posedness and asymptotics of a coordinate-free model of flame fronts
David M. Ambrose, Fazel Hadadifard, J. Douglas Wright
We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter which relates to how unstable the front might be. We fi…
Existence theory for a time-dependent mean field games model of household wealth
David M. Ambrose
We study a nonlinear system of partial differential equations arising in macroeconomics which utilizes a mean field approximation. This system together with the corresponding data,…
Global existence and analyticity for the 2D Kuramoto-Sivashinsky equation
David M. Ambrose, Anna L. Mazzucato
There is little analytical theory for the behavior of solutions of the Kuramoto-Sivashinsky equation in two spatial dimensions over long times. We study the case in which the spati…
Strong solutions for time-dependent mean field games with non-separable Hamiltonians
David M. Ambrose
We prove existence theorems for strong solutions of time-dependent mean field games with non-separable Hamiltonian. In a recent announcement, we showed existence of small, strong s…