We study the minimizers of a functional on set partitions domain $\Omega \subset R^n$ into $N$ subsets $W_j$ locally finite perimeter in $\Omega$, whose main term is $\sum_{j=1^N} \int_{\Omega \cap \partial W_j} a(x) dH^{n--1}(x)$. Here positive bounded function $a$ may for instance be related to Landscape some Schr{\o}dinger operator. prove existence through equivalence with weak formulation, ...

We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with three-field formulation weak stress symmetry. fluid flow Darcy formulation. introduce displacement and pressure Lagrange multipliers on subdomain interfaces to impose weakly continuity normal velocity, respectively. global problem reduced an interf...

In this paper we investigate the abstract hyperbolic model with time dependent stiffness and damping given by 〈ü(t), ψ〉V ∗,V + d(t; u̇(t), ψ) + a(t;u(t), ψ) = 〈f(t), ψ〉V ∗,V where V ⊂ VD ⊂ H ⊂ V ∗ D ⊂ V ∗ are Hilbert spaces with continuous and dense injections, where H is identified with its dual and 〈·, ·〉 denotes the associated duality product. We show under reasonable assumptions on the time-...

To guarantee the correction of numerical simulation programs implementing the fi-nite element method, it is necessary to formalize the mathematical notions and results that allowto establish the soundness of the method. The Lax-Milgram theorem is one of those theoreticalcornerstones: under some completeness and coercivity assumptions, it states existence and unique-ness of the s...

We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on R3`1, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below the ground state and (ii) the Krieger...

Classes with few models have 'homogeneous-universal' models This paper is concerned with a class K of models and an abstract notion of submodel ≤. Experience in first order model theory has shown the desirability of finding a 'monster model' to serve as a universal domain for K. In the original constructions of Jónsson and Fraissè, K was a universal class and ordinary substructure played the ro...

This paper is devoted to a practical implementation of deterministic particle methods for solving transport equations with discontinuous coefficients and/or initial data, and related problems. In such methods, the solution is sought in the form of a linear combination of the delta-functions, whose positions and coefficients represent locations and weights of the particles, respectively. The loc...