Anisotropic motion of a phase interface.
Application of relaxation scheme to degenerate variational inequalities
In this paper we are concerned with the solution of degenerate variational inequalities. To solve this problem numerically, we propose a numerical scheme which is based on the relaxation scheme using non-standard time discretization. The approximate solution on each time level is obtained in the iterative way by solving the corresponding elliptic variational inequalities. The convergence of the method is proved.
Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method
The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...
Approximation of crystalline dendrite growth in two space dimensions.
Approximation of parabolic equations using the Wasserstein metric
Approximation of Parabolic Equations Using the Wasserstein Metric
We illustrate how some interesting new variational principles can be used for the numerical approximation of solutions to certain (possibly degenerate) parabolic partial differential equations. One remarkable feature of the algorithms presented here is that derivatives do not enter into the variational principles, so, for example, discontinuous approximations may be used for approximating the heat equation. We present formulae for computing a Wasserstein metric which enters into the variational...
Approximation of Time-Dependent Free Boundaries
Area-minimizing integral currents with movable boundary parts of prescribed mass
Asymptotic analysis for the Ginzburg-Landau equations
Questo lavoro costituisce un survey sui problemi di limite asintotico per le soluzioni delle equazioni di Ginzburg-Landau in dimensione due. Vengono presentati essenzialmente i risultati di [BBH] e [BR] sulla formazione ed il comportamento asintotico dei vortici in un dominio bidimensionale nel caso fortemente repulsivo (large limit).
Asymptotic analysis of the -laplacian flow in an exterior domain
Asymptotic behavior for a heat conduction problem with perfect-contact boundary condition.
Asymptotic behaviour of the porous media equation in an exterior domain
Asymptotic Expansions of the Pressure and the Free Boundary for Flows through Porous Media.
Asymptotic justification of the conserved phase-field model with memory.
Asynchronous domain decomposition methods for dam and continuous casting problems
ATP Production and Necrosis Formation in a Tumour Spheroid Model
Mathematical models of tumour spheroids, proposed since the early seventies, have been generally formulated in terms of a single diffusive nutrient which is critical for cell replication and cell viability. Only recently, attempts have been made to incorporate in the models the cell energy metabolism, by considering the interplay between glucose, oxygen and lactate (or pH). By assuming glucose and lactate as the only fuel substrates, we propose a simple model for the cell ATP production which takes...
Attractors of semigroups associated with nonlinear systems for diffusive phase separation.
Bernoulli's free-boundary problem, qualitative theory and numerical approximation.
Boundary layer formation in the transition from the porous media equation to a Hele–Shaw flow
Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case.