16 citations · 18 across the 4 of their papers we have counts for
4 papers
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…
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…
Breakdown of Normal Hyperbolicity for a Family of Invariant Manifolds with Generalized Lyapunov-Type Numbers Uniformly Bounded below Their Critical Values
Dennis Guang Yang
We present three examples to illustrate that in the continuation of a family of normally hyperbolic manifolds, the normal hyperbolicity may break down as the continuation par…
An Invariant Manifold Theory for ODEs and Its Applications
Dennis Guang Yang
For a system of ODEs defined on an open, convex domain containing a positively invariant set , we prove that under appropriate hypotheses, is the graph of a functi…