Asymptotic Behavior of Gradient-Like Systems.
Jack K. Hale, Paul Massatt · Defense Technical Information Center (DTIC) · 1981
For a class of gradient evolutionary equations, we prove that the w-limit set of a bounded orbit is an equilibrium point if the dimension of the null space of the linear variational operator is no more than one. This implies the result of Matano concerning a parabolic equation in one space dimension with separated boundary conditions. The statement about gradient systems is a consequence of a more general property which has applications, for example, to the stability of traveling waves. (Author)