Catálogo de publicaciones - libros

We formulate a 1D partly dissipative moving-boundary reaction-diffusion system that describes the penetration of a reaction front into a concrete wall. We state the well-posedness of the model and the existence of non-trivial upper and lower bounds for the concentrations, speed of the interface, and shut-down time of the process. A numerical example illustrates the typical behavior of concentrations and interface penetration in a real-world application.

An adaptive phase field model for the solidification of binary alloys in two space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid.

Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh triangles having high aspect ratio whenever needed.

Numerical results are presented for dendritic growth of four dendrites.

A new model for fluid flow in diatomites [] motivates the study of a new degenerate parabolic system. We provide numerical as well as analytical evidence that there exists a free boundary, which represents the interface between the pristine rock and the damaged one.

We study the existence of positive and sign-changing solutions to the boundary value problem − Δ u = || in a bounded smooth domain Ω in ℝ, with homogeneous Dirichlet boundary condition, when is a large exponent. We find topological conditions on Ω which ensure the existence of a positive solution concentrating at exactly points as →∞. In particular, for a non-simply connected domain such a solution exists for any given ≥ 1. Moreover, for large enough, we prove the existence of two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of Ω.

We prove the long-time existence of solutions for the Mullins- Sekerka flow. We use a time discrete approximation which was introduced by Luckhaus and Sturzenhecker [Calc. Var. PDE 3 (1995)] and pass in a new weak formulation to the limit.

In this note, we prove an existence and approximation result for a class of rate-independent problems (which have already been investigated in []), by passing to the limit in a time-discretization scheme with suitably constructed variable-time steps.

In this note we summarize some results of a forthcoming paper (see []), where we examine, in particular, the long time behavior of the so-called quasistationary phase field model by using a gradient flow approach. Our strategy in fact, is inspired by recent existence results which show that gradient flows of suitable non-convex functionals yield solutions to the related quasistationary phase field systems. Thus, we firstly present the long-time behavior of solutions to an abstract non-convex gradient flow equation, by carefully exploiting the notion of by J.M. Ball and we provide some sufficient conditions for the existence of the global attractor for the solution semiflow. Then, the existence of the global attractor for a proper subset of all the solutions to the quasistationary phase field model is obtained as a byproduct of our abstract results.

The first part of this paper is an announcement of a result to appear. We apply the Aleksandrov reflection to obtain regularity and stability of the free boundaries in the problem where λ > 0 and γ > 0.

In the second part we show that the Kelvin reflection can be used in a similar way to obtain regularity of the classical obstacle problem .

The aim of this work is to develop a simulation method focused on regional economic trend. In this light, an original model, formulated by partial differential equations, will be proposed. Consequently, the existence of time-local solutions of our mathematical model will be concluded, as a transitional report in the research.

A Ginzburg-Landau type functional for a multi-phase system involving a diffuse interface description of the phase boundaries is presented with the following calibration property: Prescribed surface energies (possibly anisotropic) of the phase transitions are correctly recovered in the sense of a Γ-limit as the thickness of the diffuse interfaces converges to zero. Possible applications are grain boundary motion and solidification of alloys on which numerical simulations are presented.