The objectives of the specific effort being reported are to improve the fundamental knowledge of turbulent mixing and diffusion processes occurring in oceanic boundary layers, with special emphases on the surface mixed layer and the wave-current boundary layer in coastal oceans. In the studies of surface mixed layers, the focus is on the penetration of a mixed layer (say, driven by the wind) in...

We consider the finite element solution of the vector Laplace equation on a domain in two dimensions. For various choices of boundary conditions, it is known that a mixed finite element method, in which the rotation of the solution is introduced as a second unknown, is advantageous, and appropriate choices of mixed finite element spaces lead to a stable, optimally convergent discretization. How...

We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.

where [0, T ] ⊂ . We assume that D ⊂ 2 , f satisfies the Carathéodory conditions on (0, T ) × D , p ∈ C[0, T ] and 1/p need not be integrable on [0, T ]. Here f can have time singularities at t = 0 and/or t = T and a space singularity at x = 0. Moreover, f can change its sign. Provided f is nonnegative it can have even a space singularity at y = 0. We present conditions for the existence of sol...

The global solvability of the boundary value problem for stationarymagnetohydrodynamic equations under the Dirichlet boundary condition for the velocity and mixed boundary conditions for the magnetic field is proved. © 2014 Elsevier Ltd. All rights reserved.

The complex variable boundary element method or CVBEM is a numerical technique that can provide solutions to potential value problems in two or more dimensions by the use of an approximation function that is derived from the Cauchy integral equation in complex analysis. Given the potential values (i.e. a Dirichlet problem) along the boundary, the typical problem is to use the potential function...

In the context of the bulk-boundary correspondence we study the correlation functions arising on a boundary for different types of boundary conditions. The most general condition is the mixed one interpolating between the Neumann and Dirichlet conditions. We obtain the general expressions for the correlators on a boundary in terms of Green’s function in the bulk for the Dirichlet, Neumann and m...

The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crac...

In this paper, we study a second order differential operator with mixed nonlocal boundary conditions combined weighting integral boundary condition with another two point boundary condition. Under certain conditions on the weighting functions and on the coefficients in the boundary conditions, called non regular boundary conditions, we prove that the resolvent decreases with respect to the spec...