Equações Diferenciais

Topological Sensitivity Analysis in Damage and Fracture Mechanics

Por Marcel Xavier (LNCC, Petropolis, Brasil).

Abstract: The topological derivative is a scalar field that measures the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation, such as the insertion of holes, inclusions, source-terms or even cracks. In this work, the concept of topological derivative is applied in the context of damage and fracture mechanics. In particular, the nucleation and propagation damaging process are studied.

On the area functional and related Plateau type problems

Por Riccardo Scala (University of Rome 1, “La Sapienza”).

Abstract: We introduce the notion of area of the graph of a smooth function and the definition of the corresponding relaxed functional. We discuss some issues related to determine the domain and the exact value of it on singular maps. Finally we show how this question is related to Plateau-type problems with mixed boundary conditions and how to solve it in some specific cases.

Initial-boundary value problem for a fractional type degenerate heat equation

Por Wladimir Neves (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brasil).

Abstract: In this talk, we consider a fractional type degenerate heat equation posed in bounded domains. We show the existence of solutions for measurable and bounded non-negative initial data, and homogeneous Dirichlet boundary condition. The nonlocal diffusion effect relies on an inverse of the s-fractional Laplacian operator, and the solvability is proved for any s , 0 < s < 1.

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