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The DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Thu, 19 Jul 2018 14:49:41 GMT2018-07-19T14:49:41ZExistence and uniqueness of dynamic evolutions for a one dimensional debonding model with damping
http://preprints.sissa.it/handle/1963/35319
Existence 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.
Mon, 16 Jul 2018 00:00:00 GMThttp://preprints.sissa.it/handle/1963/353192018-07-16T00:00:00ZA minimization approach to the wave equation on time-dependent domains
http://preprints.sissa.it/handle/1963/35318
A 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.
Fri, 01 Jun 2018 00:00:00 GMThttp://preprints.sissa.it/handle/1963/353182018-06-01T00:00:00ZCompactness by maximality
http://preprints.sissa.it/handle/1963/35317
Compactness 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 $a$.
Sat, 01 Jan 2011 00:00:00 GMThttp://preprints.sissa.it/handle/1963/353172011-01-01T00:00:00ZExtended affine Weyl groups of BCD type, Frobenius manifolds and their Landau-Ginzburg superpotentials
http://preprints.sissa.it/handle/1963/35316
Extended 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.
Thu, 01 Jan 2015 00:00:00 GMThttp://preprints.sissa.it/handle/1963/353162015-01-01T00:00:00Z