Inverse free boundary problems

On Free Boundary Problems

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...

1 Inverse Boundary Value Problems in Applications

Highlights of Results. Here are some of the main results of my research in recent years: (i) Together with my collaborators, we have performed constructive mathematical analysis on elliptic inverse problems in quantitative photoacoustic tomography (QPAT)[8]. The analysis led to not only uniqueness and stability results on the inverse problems but also a direct reconstruction method that is non-...

Inverse Sturm-Liouville problems with a Spectral Parameter in the Boundary and transmission conditions

In this manuscript, we study the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. By defining  a new Hilbert space and  using its spectral data of a kind, it is shown that the potential function can be uniquely determined by part of a set of values of eigenfunctions at som...

Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions

This paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new...