The Mullins Sekerka model is a nonlocal evolution model for hypersurfaces, which arises as a singular limit for the Cahn Hilliard equation. We show that classical solutions exist globally and tend to spheres exponentially fast, provided that they are close to a sphere initially. Our analysis is based on center manifold theory and on maximal regularity. 1998 Academic Press

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

A commonly used mathematical model for jet engines that captures the ow behavior of a compression system, known as the viscous Moore-Greitzer PDE model, consists of a PDE and two ODEs. The PDE describes the behavior of disturbances in the inlet region of the compression system, and the two ODEs describe the coupling of the disturbances with the mean ow. In this paper, we study this full-order m...

We study the behaviour of solutions to nonlinear autonomous functional differential equations of mixed type in the neighbourhood of an equilibrium. We show that all solutions that remain sufficiently close to an equilibrium can be captured on a finite dimensional invariant center manifold, that inherits the smoothness of the nonlinearity. In addition, we provide a Hopf bifurcation theorem for s...

This is the second paper of a series of three on the regularity of higher codimension area minimizing integral currents. Here we perform the second main step in the analysis of the singularities, namely the construction of a center manifold, i.e. an approximate average of the sheets of an almost flat area minimizing current. Such a center manifold is accompanied by a Lipschitz multivalued map o...