5 citations · 17 across the 9 of their papers we have counts for
6 papers · 1 filter
Construction of eternal solutions for a semilinear parabolic equation
Michael Robinson
Eternal solutions of parabolic equations (those which are defined for all time) are typically rather rare. For example, the heat equation has exactly one eternal solution -- the tr…
Eternal solutions and heteroclinic orbits of a semilinear parabolic equation
Michael Robinson
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…
Classification of connecting solutions of semilinear parabolic equations
Michael Robinson
For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large class of these equations, we show that some of th…
Instability of an equilibrium of a partial differential equation
Michael Robinson
A nonlinear parabolic differential equation with a quadratic nonlinearity is presented which has at least one equilibrium. The linearization about this equilibrium is asymptoticall…
Instability of an equilibrium with negative definite linearization
Michael Robinson
A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum whi…
IMEX method convergence for a parabolic equation
Michael Robinson
Although implicit-explicit (IMEX) methods for approximating solutions to semilinear parabolic equations are relatively standard, most recent works examine the case of a fully discr…