SDLThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2018-11-24T00:57:19Z2018-11-24T00:57:19ZWeak formulation of elastodynamics in domains with growing cracksTasso, Emanuelehttp://preprints.sissa.it/handle/1963/353282018-11-23T01:00:28Z2018-11-01T00:00:00ZWeak formulation of elastodynamics in domains with growing cracks
Tasso, Emanuele
In this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n − 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality.
We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.
2018-11-01T00:00:00ZOn Krylov solutions to infinite-dimensional inverse linear problemsCaruso, NoeMichelangeli, AlessandroNovati, Paolohttp://preprints.sissa.it/handle/1963/353272018-11-21T01:00:34Z2018-11-01T00:00:00ZOn Krylov solutions to infinite-dimensional inverse linear problems
Caruso, Noe; Michelangeli, Alessandro; Novati, Paolo
We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of the considered inverse problem. The presentation is based on theoretical results together with a series of model examples, and it is corroborated by specific numerical experiments.
2018-11-01T00:00:00ZTruncation and convergence issues for bounded linear inverse problems in Hilbert spaceCaruso, NoeMichelangeli, AlessandroNovati, Paolohttp://preprints.sissa.it/handle/1963/353262018-11-21T01:00:28Z2018-01-01T00:00:00ZTruncation and convergence issues for bounded linear inverse problems in Hilbert space
Caruso, Noe; Michelangeli, Alessandro; Novati, Paolo
We present a general discussion of the main features and issues
that (bounded) inverse linear problems in Hilbert space exhibit when the dimension
of the space is infinite. This includes the set-up of a consistent notation
for inverse problems that are genuinely infinite-dimensional, the analysis
of the finite-dimensional truncations, a discussion of the mechanisms why the
error or the residual generically fail to vanish in norm, and the identification
of practically plausible sufficient conditions for such indicators to be small in
some weaker sense. The presentation is based on theoretical results together
with a series of model examples and numerical tests.
2018-01-01T00:00:00ZCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equationsBianchini, StefanoSpinolo, Laurahttp://preprints.sissa.it/handle/1963/353252018-10-17T00:00:27Z2018-10-16T00:00:00ZCharacteristic boundary layers for mixed hyperbolic systems in one space dimension and applications to the Navier-Stokes and MHD equations
Bianchini, Stefano; Spinolo, Laura
We provide a detailed analysis of the boundary layers for mixed hyperbolic-parabolic systems in one space dimension and small amplitude regimes. As an application of our results, we describe the solution of the so-called boundary Riemann problem recovered as the zero viscosity limit of the physical viscous approximation. In particular, we tackle the so called doubly characteristic case, which is considerably more demanding from the technical viewpoint and occurs when the boundary is characteristic for both the
mixed hyperbolic-parabolic system and for the hyperbolic system obtained by neglecting the second order terms. Our analysis applies in particular to the compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both positive and null conductivity. In these cases, the doubly characteristic case occurs when the velocity is close to 0. The analysis extends to non-conservative systems.
2018-10-16T00:00:00Z