Existence of periodic solution for a Cahn-Hilliard/Allen-Cahn equation in two space dimensions
Changchun Liu Hui Tang

In this paper, we discuss the existence of the periodic solutions of a Cahn-Hillard/Allen-Cahn equation which is introduced as a simplification of multiple microscopic mechanisms model in cluster interface evolution. Based on the Schauder type a priori estimates, which here will be obtained by means of a modified Campanato space, we prove the existence of time-periodic solutions in two space dimensions. The uniqueness of solutions is also discussed.

keywords: Cahn-Hilliard/Allen-Cahn equation existence uniqueness periodic solution
Hopf bifurcation for a spatially and age structured population dynamics model
Zhihua Liu Hui Tang Pierre Magal
This paper is devoted to the study of a spatially and age structured population dynamics model. We study the stability and Hopf bifurcation of the positive equilibrium of the model by using a bifurcation theory in the context of integrated semigroups. This problem is a first example for Hopf bifurcation for a spatially and age/size structured population dynamics model. Bifurcation analysis indicates that Hopf bifurcation occurs at a positive age/size dependent steady state of the model. The results are confirmed by some numerical simulations.
keywords: integrated semigroups. Hopf bifurcation population dynamics spatially and age/size structure

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