16 citations · 33 across the 6 of their papers we have counts for
6 papers
Well-posedness of fully nonlinear KdV-type evolution equations
Timur Akhunov, David M. Ambrose, J. Douglas Wright
We study the well-posedness of the initial value problem for fully nonlinear evolution equations, where may depend on up to the first three spatial derivatives of…
Existence theory for magma equations in dimension two and higher
David M. Ambrose, Gideon Simpson, J. Douglas Wright +1
We examine a degenerate, dispersive, nonlinear wave equation related to the evolution of partially molten rock in dimensions two and higher. This simplified model, for a scalar fie…
Global bifurcation theory for periodic traveling interfacial gravity-capillary waves
David M. Ambrose, Walter A. Strauss, J. Douglas Wright
We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-n…
Nonexistence of small doubly periodic solutions for dispersive equations
David M. Ambrose, J. Douglas Wright
We study the question of existence of time-periodic, spatially periodic solutions for dispersive evolution equations, and in particular, we introduce a framework for demonstrating…
Dispersion vs. anti-diffusion: well-posedness in variable coefficient and quasilinear equations of KdV-type
J. Douglas Wright, David M. Ambrose
We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial d…
Ill-posedness of degenerate dispersive equations
David M. Ambrose, Gideon Simpson, J. Douglas Wright +1
In this article we provide numerical and analytical evidence that some degenerate dispersive partial differential equations are ill-posed. Specifically we study the K(2,2) equation…