Integral boundary conditions in phase field models

Phase-field models for free-boundary problems

Phase-field models are very attractive in view of their numerical simplicity. With only a few lines of code, one can model complex physical situations such as dendritic growth. From this point of view, they constitute very interesting tools for teaching purposes at graduate level. The main difficulty with these models is in their formulation, which incorporates the physical ingredients in a sub...

Second-Order Boundary Value Problem with Integral Boundary Conditions

Fuzzy Solutions for Boundary Value Problems with Integral Boundary Conditions

The Banach fixed point theorem is used to investigate the existence and uniquenness of fuzzy solutions for a class of second order nonlinear boundary value problems with integral boundary conditions.

Higher order multi-point fractional boundary value problems with integral boundary conditions

In this paper, we concerned with positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions. We establish the criteria for the existence of at least one, two and three positive solutions for higher order m-point nonlinear fractional boundary value problems with integral boundary conditions by using a result from the theory of fixed...

Phase retrieval using boundary conditions

It is shown that a priori knowledge of the edges of an object is not sufficient to ensure that it can be uniquely reconstructed from the modulus of its Fourier transform (or from its autocorrelation function). Furthermore, even in those cases for which the ultimate solution is unique, in intermediate steps in the solution by the recursive Hayes-Quatieri algorithm there can be ambiguities. An ex...