Abstract The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. ill-posedness of this tackled by means variational form mollification. This approach proved to be consistent, and proposed numerical simulations are quite promising.

ASYMPTOTIC VALUES AND THE GROWTH OF ANALYTIC FUNCTIONS IN SPIRAL DOMAINS J . E . BRENNAN AND A . L . VOLBERG In this note we present a simple proof of a theorem of Hornblower which characterizes those functions analytic in the open unit disk having asymptotic values at a dense set in the boundary. Our method is based on a kind of ó-mollification and may be of use in other problems as well .

This work develops and applies the concept of mollification in order to smooth out highly oscillatory exponentials. This idea, known for quite a while in the mathematical community (mollifiers are a means to smooth distributions), is new to numerical Quantum Field Theory. It is potentially very useful for calculating phase transitions (highly oscillatory integrands in general), for computations...

We show that a compact feasible set of a standard semi-infinite optimization problem can be approximated arbitrarily well by a level set of a single smooth function with certain regularity properties. This function is constructed as the mollification of the lower level optimal value function. Moreover, we use correspondences between KarushKuhn-Tucker points of the original and the smoothed prob...

This paper deals with the reliable and efficient numerical identification of parameters defining the flux function and the diffusion coefficient of a strongly degenerate parabolic partial differential equation (PDE), which is the basis of a mathematical model for sedimentation-consolidation processes. A zero-flux initial-boundary value problem (IBVP) posed for this PDE describes the settling of...

The mollification method and the numerical solution of ill-posed problems / by Diego A. Murio. p. cm. PREFACE During the last 20 years, the subject of ill-posed problems has expanded from a collection of individual techniques to a highly developed and rich branch of applied mathematics. This textbook essentially builds, from basic mathematical concepts, the understanding of the most important a...

In this paper, we construct local and global solutions to the K\"ahler-Ricci flow from a non-collapsed K\"ahler manifold with curvature bounded below. Combines mollification technique of McLeod-Simon-Topping, show that Gromov-Hausdorff limit sequence complete noncompact manifolds orthogonal bisectional Ricci below is homeomorphic complex manifold. We also use it study structure nonnegative curv...