Non-Existence and Uniqueness Results for the Extended Fisher-Kolmogorov Equation. Modelling, Analysis and Simulation. Modelling, Analysis and Simulation.

摘要

Starting with the work of Toland and Hofer & Toland, a technique has been developed to exploit the special structure of certain Hamiltonian systems with an indefinite kinetic energy. This technique provides a geometrical tool akin to the phase plane analysis that has proven so powerful in the case of two-dimensional dynamical systems. Geometrical properties of a pseudo-phase space of reduced dimension are used to prove existence, uniqueness, and many qualitative properties of solutions.