‎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...

An efficient, non-stiff boundary integral method for the initial value problem for interfacial Darcy flow (which is a model of porous media flow) in three space dimensions is presented. We consider a ‘doubly-periodic’ interface separating two fluids, with surface tension present at the boundary. Surface tension introduces high order (i.e., high derivative) terms in the governing equation, and t...

Abstract:The two point boundary value problems with Neumann and mixed Robbin’s boundary conditions have great importance in chemical engineering, deflection of beams etc. It is not easy task to solve numerically such type of problems. In this paper, Galerkin-finite element method is proposed for the numerical solution of the boundary value problem having mixed Robbin’s and Dirichlet’s condition...

Motivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography that appears as an important application in Underwater Acoustics, we analyze a general Schrödinger-type equation posed on two-dimensional variable domains with mixed boundary conditions. The resulting initialand boundary-value problem is transformed into an equivalent one posed on a ...

We consider the mixed boundary value problem for the Stokes and steady NavierStokes equations in two-dimensional domain with corner points on boundary, where the boundary conditions change their type. Our goal is to prove some regularity results near corner points, where the boundary conditions change.