SDLThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.http://preprints.sissa.it:80/xmlui2018-07-19T15:48:41Z2018-07-19T15:48:41ZExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with dampingRiva, FilippoNardini, Lorenzohttp://preprints.sissa.it/handle/1963/353192018-07-17T00:00:25Z2018-07-16T00:00:00ZExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping
Riva, Filippo; Nardini, Lorenzo
In this paper we analyse a one-dimensional debonding model for a thin film peeled
from a substrate when friction is taken into account. It is described by the weakly damped wave equation whose domain, the debonded region, grows according to a Griffth's criterion. Firstly we prove that the equation admits a unique solution when the evolution of the debonding front is assigned. Finally we provide an existence and uniqueness result for the coupled problem given by the wave equation together with Griffth's criterion.
2018-07-16T00:00:00ZA minimization approach to the wave equation on time-dependent domainsDal Maso, GianniDe Luca, Luciahttp://preprints.sissa.it/handle/1963/353182018-06-06T00:00:26Z2018-06-01T00:00:00ZA minimization approach to the wave equation on time-dependent domains
Dal Maso, Gianni; De Luca, Lucia
We prove the existence of weak solutions to the homogeneous wave equation
on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi
and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable
functionals in space-time.
2018-06-01T00:00:00ZCompactness by maximalityZagatti, Sandrohttp://preprints.sissa.it/handle/1963/353172018-05-25T00:00:33Z2011-01-01T00:00:00ZCompactness by maximality
Zagatti, Sandro
We derive a compactness property in the Sobolev space $W^{1,1}(\O)$ in order to study the Dirichlet problem for the eikonal equation \begin{displaymath} \begin{cases} \ha |\n u(x)|^2 - a(x) = 0 & \ \textrm{in} \ \O\cr u(x)=\varphi(x) & \ \textrm{on} \ \partial \O, \end{cases} \end{displaymath} without continuity assumptions on the map $a$.
2011-01-01T00:00:00ZExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentialsDubrovin, BorisStrachan, Ian A.B.Zhang, YoujinZuo, Dafenghttp://preprints.sissa.it/handle/1963/353162018-05-24T00:00:37Z2015-01-01T00:00:00ZExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
Dubrovin, Boris; Strachan, Ian A.B.; Zhang, Youjin; Zuo, Dafeng
For the root systems of type Bl, Cl and Dl, we generalize the result of [7] by showing the existence of Frobenius manifold structures on the orbit spaces of the extended affine Weyl groups that correspond to any vertex of the Dynkin diagram instead of a particular choice made in [7]. It also depends on certain additional data. We also construct LG superpotentials for these Frobenius manifold structures.
2015-01-01T00:00:00Z