A Sequence of Order Relations: Encoding Heteroclinic Connections in Scalar Parabolic PDE

Heteroclinic orbits of semilinear parabolic equations

Parabolic Pde with Hysteresis

Our objective here is to describe some results on the well-posedness of initial-boundary-value problems for a nonlinear parabolic partial diierential equation with memory eeects and with general boundary conditions. The system consists of a general porous medium equation together with a family of ordinary diierential equations subject to constraints. Such a system includes a very general class ...

The Genesis Trajectory and Heteroclinic Connections

Genesis will be NASA's first robotic sample return mission. The purpose of this mission is to collect solar wind samples for two years in an £ 1 halo orbit and return them to the Utah Test and Training Range {UTTR) for mid-air retrieval by helicopters. To do this, the Genesis spacecraft makes an excursion into the region around £ 2 . This transfer between £ 1 and L 2 requires no deterministic m...

Explorer A Hyperbolic PDE with Parabolic Behavior

In this paper we present a hyperbolic partial differential equation (PDE) in one space and one time dimension. This equation arose in a study of numerical schemes for simulating evolving river topographies. The solution of this PDE, whose initial data are specified along a characteristic, is very similar to that of the canonical diffusion equation. This interesting example provides insight into...

Eternal Solutions and Heteroclinic Orbits of a Semilinear Parabolic Equation

This dissertation describes the space of heteroclinic orbits for a class of semilinear parabolic equations, focusing primarily on the case where the nonlinearity is a second degree polynomial with variable coefficients. Along the way, a new and elementary proof of existence and uniqueness of solutions is given. Heteroclinic orbits are shown to be characterized by a particular functional being f...