In this paper we consider Galerkin-finite element methods that approximate the solutions of initial-boundary-value problems in one space dimension for parabolic and SchrÃ¶dinger evolution equationsâ€¦ (More)

We describe the joint motion of multiple kinks or interfaces for the one-dimensional Cahn-Hilliard equation on a bounded interval perturbed by small additive noise The approach is based on anâ€¦ (More)

We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polarâ€¦ (More)

We consider Cahn-Hilliard equations with external forcing terms. Energy decreasing and mass conservation might not hold. We show that level surfaces of the solutions of such generalized Cahn-Hilliardâ€¦ (More)

We analyze the evolution of multi-dimensional normal graphs over the unit sphere under volume preserving mean curvature flow and derive a non-linear partial differential equation in polarâ€¦ (More)

Here we present the quantitative approximation of positive sublinear operators to the unit operator. These are given a precise Choquet integral interpretation. Initially we start with the study ofâ€¦ (More)

Motivated by the paraxial narrowâ€“angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundaryvalue problem for a general SchrÃ¶dinger-typeâ€¦ (More)

Motivated by the paraxial narrowâ€“angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a generalâ€¦ (More)

The standard â€˜parabolicâ€™ approximation to the Helmholtz equation is used in order to model long-range propagation of sound in the sea in the presence of cylindrical symmetry in a domain with a rigidâ€¦ (More)