We apply our recently developed global Hopf bifurcation theory to examine global continuation with respect to the parameter for periodic solutions of functional differential equationswith state-dependent delay.We give sufficient geometric conditions to ensure the uniform boundedness of periodic solutions, obtain an upper bound of the period of nonconstant periodic solutions in a connected compo...

We show short time existence and uniqueness of C solutions to the mean curvature flow with obstacles, when the obstacles are of class C. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.

We have been working on a long term program to construct the first time-periodic solutions of the compressible Euler equations. Our program from the start has been to construct the simplest periodic wave structure, and then tailor the analysis in a rigorous existence proof to the explicit structure. In [26] have found the periodic structure, in [27, 28] we showed that linearized solutions with ...

We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their wellposedness and describe some qualitative properties of their solutions, including boundedness, stability, or almost periodicity. In particular, we are able to characterize the analyticity of ...

We show short time existence and uniqueness of C solutions to the mean curvature ow with obstacles, when the obstacles are of class C. If the initial interface is a periodic graph we show long time existence of the evolution and convergence to a minimal constrained hypersurface.

For the complete higher order differential equation u(t) = Σn−1 k=0Aku (t) + f(t), t ∈ R (*) on a Banach space E, we give a new definition of mild solutions of (*). We then characterize the regular admissibility of a translation invariant subspace M of BUC(R,E) with respect to (*) in terms of solvability of the operator equation Σn−1 j=0AjXD j −XD = C. As application, almost periodicity of mild...