The propagation of torsional waves in a prestressed fiber-reinforced half-space under the effect of magnetic field and gravity has been discussed. The problem has been solved analytically using Whittaker function to obtain the exact solution frequency equations. Numerical results for stress, gravity and magnetic field are given and illustrated graphically. Comparisons are made with the results ...

Numerous models of industrial processes such as diffusion in glassy polymers or solidification phenomena, lead to general one-phase free boundary value problems with phase onset. In this paper we develop a framework viable to prove global existence and stability of planar solutions to one such multidimensional model whose application is in controlled-release pharmaceuticals. We utilize a bounda...

A sharp interface model of crack propagation as a phase transition process is discussed. We develop a multipole expansion technique to solve this free boundary problem numerically. We obtain steady state solutions with a self-consistently selected propagation velocity and shape of the crack, provided that elastodynamic effects are taken into account. Also, we find a saturation of the steady sta...

In this paper we study a free{boundary problem in a multicomponent domain. Our study was motivated by the mathematical modelling of dermal and transdermal drug delivery, where the multilayered skin model was considered. At the interface connecting two components the conservation of the ux and Nernst's distribution law hold and it is supposed that in any component there is a positive minimum con...

In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz and the free boundary is analytic away from a singular set with Hausdorff dimension at most n− 8. Mathematics Subject Classification (2000): 49Q20

In this paper we are interested in a free boundary problem whith a motion law involving the mean curvature term of the free boundary. Viscosity solutions are introduced as a notion of global-time solutions past singularities. We show the comparison principle for viscosity solutions, which yields the existence of minimal and maximal solutions for given initial data. We also prove uniqueness of t...

We study a two-point free boundary problem for a quasilinear parabolic equation. This problem arises in the model of flame propagation in combustion theory. It also arises in the study of the motion of interface moving with curvature in which the studied problem is confined in the conical region bounded by two straight lines and the interface has prescribed touching angles with these two straig...

The ability of a large variety of eukaryotic cells to actively move along different substrates plays a vital role in many biological processes. A key player in these processes is the cytoskeleton. In [7] we introduced a minimal hyperbolic-parabolic model for the reorganization of the actin cytoskeleton of a generic cell resting on a flat substrate and turning into a polarized state upon some ex...

The purpose of this work is to present an error analysis of the numerical approximation by a finite element method of a free-surface problem. The analysis has been done in an abstract model which has many of the features of a free-surface problem for a viscous liquid. We study in this paper how the numerical approximation of the free boundary affects the approximation of the other variables of ...

We study a degenerate nonlinear parabolic equation with moving boundaries which arises in the study of the technique of contour enhancement in image processing. In order to obtain mass concentration at the contour, singular data must be imposed at the free boundary, leading to a non-standard free boundary problem. Our main results are: (i) the well-posedness for the singular problem, without mo...