Conferència presentada dins el marc de la GLOBAL School on PDEs: layers and dislocations (Barcelona, UPC, 18-22 juny 2007).

Phase-field models for brittle fracture consider smeared representations of cracks, which are described by a continuous field that varies abruptly in the transition zone between unbroken and broken states. Computationally, ...

We study the equation $$-\Delta u=\lambda\left(\frac{e^u}{\int_\oep e^u}- \frac{1}{|\oep|}\right)\quad \text{in }\oep$$ for $u\in E$, where $E = \{ u \in H^1(\oep): u \hbox{ is doubly periodic}, \int_{\oep} u = 0 \}$ and ...

We present in this paper a pressure stabilized, finite element method for the numerical approximation of three-dimensional, non-hydrostatic mesoscale ocean flows. The model considered here incorporates surface wind ...

This work is devoted to review the modern geometric description of the Lagrangian and Hamiltonian formalisms of the Hamilton–Jacobi theory. The relation with the “classical” Hamiltonian approach using canonical transformations ...

Se trata de hallar el campo magnético producido por un hilo infinitesimal de corriente cuando hay placas, paralelas entre ellas, de distintos materiales. Para ello con las ecuaciones de Maxwell se obtiene una EDP que se ...

It is important that the estimates of the parameters of an autoregressive moving-average (ARMA) model should satisfy the conditions of stationarity and invertibility. It can be shown that the unconditional maximum-likelihood ...

In this dissertation we present an introduction to nonlocal operators, and in particular, we study the fractional heat equation, which involves the fractional Laplacian of order 2s. In the first chapters we make a review ...

We notice that some well-known homotopy operators due to Skoda et. al. for the $\bar\partial$-complex in the ball actually give the boundary values of the canonical homotopy operators with respect to certain weighted Bergman ...