The propagation of surface waves in a fluid- saturated porous isotropic layer over a semi-infinite homogeneous elastic medium with an irregularity for free and rigid interfaces have been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for Love waves is derived by simple mathematical techniques followed by Fourier transformations.  It can be seen t...

Given compactly supported 0 ≤ f, g ∈ L1(R), the problem of transporting a fraction m ≤ min{‖f‖L1 , ‖g‖L1} of the mass of f onto g as cheaply as possible is considered, where cost per unit mass transported is given by a cost function c, typically quadratic c(x,y) = |x − y|/2. This question is shown to be equivalent to a double obstacle problem for the Monge-Ampère equation, for which sufficient ...

Two problems in control theory, one with state constraints and the other with control constraints, have been approximated by the finite element method. This discretization has been applied to both the primal and the dual formulation, in order to make a number of observations and comparisons: 1. The rate of convergence as the grid interval h is decreased, for polynomial elements of different deg...

In this paper we consider a free boundary problem which describes contact angle dynamics on inhomogeneous surface. We obtain an estimate on convergence rate of the free boundaries to the homogenization limit in periodic media. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.

Consider the solution of a boundary-value problem for steady linear elasticity in which the computational domain contains one or several holes with traction-free boundaries. The presence of holes in the material can be approximated using a weak material; that is, the relative density of material ρ is set to 0 < = ρ 1 in the hole region. The weak material approach is a standard technique in the ...

We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions , we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned ab...

We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Hauswirth, Hélein and Pacard, whose free boundary has the shape of a double hairp...

The problem of minimizing /[Vu|2 + q2(x)\2(v)] dx in an appropriate class of functions v is considered. Here q(x) ¥= 0 and A2(t>) = X2 if v < 0, = X22 if v > 0. Any minimizer u is harmonic in {u ¥= 0} and | Vu|2 has a jump a2(x)(\]-\22) across the free boundary [u ¥= 0). Regularity and various properties are established for the minimizer u and for the free boundary. Introduction. In this paper ...