Stable and Unstable Manifolds for Hyperbolic Bi-Semigroups

On behalf of the Department of Mathematics and Statistics, AUS College of Arts and Sciences, you are cordially invited to a seminar to be conducted by Dr. Mohamed Sami ElBialy from the University of Toledo (Ohio, USA) and currently at RIT-Dubai.

Abstract:

We show the existence of local Lipschitzian stable and unstable manifolds for the ill-posed problem of perturbations of hyperbolic bi-semigroups. A bi-semigroup consists of two semigroups, one defined for t>=0, the other for t<= 0. When coupled with nonlinear terms, the system becomes ill-posed. We do not assume backward nor forward uniqueness of solutions, nor do we assume global smallness conditions on the nonlinearities. We introduce what we call dichotomous flows which recover the symmetry between the past and the future and prove a stable manifold theorem.

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