European Journal of Applied Mathematics - Current Issue

Volume 19 Issue 06

Mon, 01 Dec 2008 00:00:00 GMT

European Journal of Applied Mathematics, Volume 19 Issue 06

Since 2008 EJAM surveys have been expanded to cover Applied and Industrial Mathematics. Coverage of the journal has been strengthened in probabilistic applications, while still focusing on those areas of applied mathematics inspired by real-world applications, and at the same time fostering the development of theoretical methods with a broad range of applicability. Survey papers contain reviews of emerging areas of mathematics, either in core areas or with relevance to users in industry and other disciplines. Research papers may be in any area of applied mathematics, with special emphasis on new mathematical ideas, relevant to modelling and analysis in modern science and technology, and the development of interesting mathematical methods of wide applicability.

A two-fluid model for tissue growth within a dynamic flow environment

Research Articles
R. D. O'DEA, S. L. WATERS, H. M. BYRNE,
European Journal of Applied Mathematics, Volume 19 Issue 06 , pp 607-634

Abstract
We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571 89).

Reconstruction in the inverse crack problem by variational methods

Research Articles
LUCA RONDI,
European Journal of Applied Mathematics, Volume 19 Issue 06 , pp 635-660

Abstract
We deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements goes to zero. We further notice that we use the Shah functional due to Ambrosio and Tortorelli as the required regularization term.

Pulsating wave for mean curvature flow in inhomogeneous medium

Research Articles
N. DIRR, G. KARALI, N. K. YIP,
European Journal of Applied Mathematics, Volume 19 Issue 06 , pp 661-699

Abstract
We prove the existence and uniqueness of pulsating waves for the motion by mean curvature of an n-dimensional hypersurface in an inhomogeneous medium, represented by a periodic forcing. The main difficulty is caused by the degeneracy of the equation and the fact the forcing is allowed to change sign. Under the assumption of weak inhomogeneity, we obtain uniform oscillation and gradient bounds so that the evolving surface can be written as a graph over a reference hyperplane. The existence of an effective speed of propagation is established for any normal direction. We further prove the Lipschitz continuity of the speed with respect to the normal and various stability properties of the pulsating wave. The results are related to the homogenisation of mean curvature flow with forcing.

Finding symmetries by incorporating initial conditions as side conditions

Research Articles
JOANNA GOARD,
European Journal of Applied Mathematics, Volume 19 Issue 06 , pp 701-715

Abstract
It is generally believed that in order to solve initial value problems using Lie symmetry methods, the initial condition needs to be left invariant by the infinitesimal symmetry generator that admits the invariant solution. This is not so. In this paper we incorporate the imposed initial value as a side condition to find from which solutions satisfying the initial value can be recovered, along with the corresponding symmetry generator.

On periodic Stokesian Hele-Shaw flows with surface tension

Research Articles
J. ESCHER, B.-V. MATIOC,
European Journal of Applied Mathematics, Volume 19 Issue 06 , pp 717-734

Abstract
In this paper we consider a 2 -periodic and two-dimensional Hele-Shaw flow describing the motion of a viscous, incompressible fluid. The free surface is moving under the influence of surface tension and gravity. The motion of the fluid is modelled using a modified version of Darcy's law for Stokesian fluids. The bottom of the cell is assumed to be impermeable. We prove the existence of a unique classical solution for a domain which is a small perturbation of a cylinder. Moreover, we identify the equilibria of the flow and study their stability.