Partial Neutral Functional Differential Equations with Infinite Delay

In this book, we deal with a class of partial (neutral) functional differential equations with infinite delay. We, first, present some results on functional analysis which are useful. We give an axiomatic presentation of the fundamental theory of the phase space and recall some results on integrated semigroups theory. Then, we discuss existence and regularity of solutions in the case where the nonlinear part F is continuous and Lipschitzian with respect to the second variable. After that, we study existence and regularity of solutions in the case where F is locally Lipschitzian. In the case where global existence is verified, we prove that the solution defines a semigroup that satisfies the translation property. This permits us to study stability of an equilibrium point and prove existence of a global attractor. Besides, we give other sufficient conditions for existence and regularity of solutions, and in the autonomous case; we study stability of an equilibrium point. At the end, we investigate existence of periodic solutions in the case where F is periodic in t.

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Hassane Bouzahir was born on September 22, 1974. He obtained a M.S. in Dynamical Systems and a PhD in Delay Differential Equations, respectively, in November 1997 and April 2001. His research fields include also hybrid systems and the applications of mathematics. He has more than 10 years experience teaching different mathematics courses.