Title：Existence of wave trains for the Gurtin-MacCamy equation
Speaker：Professor Pierre Magal， University Bordeaux，France
Time：January 2，2020（Thursday）10:00-11:00  
Location：School of Mathematics 425
Abstract: This work is mainly motivated by the study of periodic wave train solutions for the so-called Gurtin-MacCamy equation. To that aim we construct a smooth center manifold for a rather general class of abstract second order semi-linear differential equations involving non-densely defined operators. We revisit results on commutative sums of linear operators using the integrated semigroup theory. These results are used to reformulate the notion of the weak solutions of the problem. We also derive a suitable fixed point formulation for the graph of the local center manifold that allows us to conclude to the existence and smoothness of such a local invariant manifold. Then we derive a Hopf bifurcation theorem for second order semi-linear equations. This result is applied to study the existence of periodic wave trains for the Gurtin-MacCamy problem, that is for a class of non-local age structured equations with diffusion.