In this paper, we combine results on extensions of operators with recent results on the relation between the M -function and the spectrum, to examine the spectral behaviour of boundary value problems. M -functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the op...

Sufficient conditions are given for a generalized viscosity solution of an elliptic boundary value problem to satisfy the boundary values in the strong sense.

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

Exact solutions for ice sheet equations can and should play an important role in numerical model validation. In constructing a time-dependent exact solution to the thermocoupled shallow ice approximation, it was discovered that the existing analytical steady solutions are a poor basis [1]. This prompted a search for cleaner steady solutions to the isothermal shallow ice equation. In particular,...

We present our recent results on the mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the potential flow equation. The shock diffraction problem can be formulated as an initial-boundary value problem, which is invariant under the selfsimilar scaling. Then, by employing its self-similar invariance, the problem is reduced ...