1,721,004 research outputs found
Wave equation in domains with many small obstacles
No full textWe study the behaviour of solutions of relaxed wave equations with Dirichlet boundary conditions corresponding to a gamma-convergent sequence of measures. The model case is that of a sequence of domains with many small obstacles. Convergence results are proved for the solutions on finite time intervals
Scattering in domains with many small obstacles
No full textWe study the behaviour of the wave operators for the relaxed wave equations corresponding to a gamma-convergent sequence of measures. The model case is that of a sequence of domains with many small obstacles
Some Problems in the Asymptotic Analysis of Partial Differential Equations in Perforated Domains
No full textNonlocal approximation of non-isotropic free-discontinuity problems
No full textWe prove that a class of free-discontinuity problems with nonisotropic bulk and surface energy densities is approximated, in the sense of Gamma-convergence, by suitable families of nonlocal integral functionals. Some connections with the Wulff set are also pointed out
A note on the integral representation of functionals in the space SBD(Ω)
No full textIn this paper we study the integral representation in the space SBD of special functions with bounded deformation of some L1-norm lower semicontinuous functionals invariant with respect to rigid motions
Scaling in fracture mechanics by BaŽant law: From finite to linearized elasticity
Full text linkWe consider crack propagation in brittle nonlinear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains nΩ on which the imposed boundary conditions scale according to Bazant's law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n → ∞) to the evolution of a crack in a brittle linear-elastic materia
A variational model for the quasi-static growth of fractional dimensional brittle fractures
No full textWe propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as F-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero
Finite element approximation of non-isotropic free-discontinuity problems
No full textWe study a discretization procedure, using finite elements, for a class of non-isotropic free-discontinuity problems based on the non-local approximation we proposed in a previous paper
Calculus of Variations and Applications: international conference to celebrate Gianni Dal Maso's 65th Birthday, 2020: 27 January - 2 February, Trieste (Italy)
No full textAn International Conference held in SISSA to celebrate Gianni Dal Maso's 65th Birthday and an exceptional opportunity to present the state of the art of modern methods in the Calculus of Variations and their applications and to stimulate exchange of ideas and knowledge, through a rich selection of talks by leading experts in the field. (2020-01-27
Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth
Full text linkWe prove existence and multiplicity of subharmonic solutions for Hamiltonian systems obtained as perturbations of N planar uncoupled systems which, e.g., model some type of asymmetric oscillators. The nonlinearities are assumed to satisfy Landesman–Lazer conditions at the zero eigenvalue, and to have some kind of sublinear behaviour at infinity. The proof is carried out by the use of a generalized version of the
Poincaré–Birkhoff Theorem. Different situations, including Lotka-Volterra systems, or systems with singularities, are also illustrate
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