In this paper we present a one-dimensional model of a dynamic peeling test for a thin film, where the wave equation is coupled with a Griffith criterion for the propagation of the debonding front. Our main results provide existence and uniqueness for the solution to this coupled problem under different assumptions on the data.

10aDynamic debonding10aDynamic energy release rate10aDynamic fracture10aGriffith's criterion10aMaximum dissipation principle10aWave equation in time-dependent domains1 aDal Maso, Gianni1 aLazzaroni, Giuliano1 aNardini, Lorenzo uhttp://www.sciencedirect.com/science/article/pii/S002203961630177201267nas a2200121 4500008004100000245009800041210006900139520082000208100002101028700002601049700001901075856005101094 2015 en d00aExistence for constrained dynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for constrained dynamic Griffith fracture with a weak 3 aThere are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica uhttp://urania.sissa.it/xmlui/handle/1963/3504500316nas a2200121 4500008004100000245001400041210001400055260001300069100002000082700002100102700002000123856005100143 2014 en d00aEditorial0 aEditorial bSpringer1 aCiliberto, Ciro1 aDal Maso, Gianni1 aVetro, Pasquale uhttp://urania.sissa.it/xmlui/handle/1963/3471200628nas a2200109 4500008004100000245003900041210003800080260004800118520029500166100002100461856003600482 2011 en d00aEnnio De Giorgi and Γ-convergence0 aEnnio De Giorgi and Γconvergence bAmerican Institute of Mathematical Sciences3 aΓ-convergence was introduced by Ennio De Giorgi in a series of papers published between 1975 and 1983. In the same years he developed many applications of this tool to a great variety of asymptotic problems in the calculus of variations and in the theory of partial differential equations.1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/530801548nas a2200157 4500008004300000245008600043210006900129260005100198300001400249490000800263520101800271100002101289700002201310700002201332856003601354 2011 en_Ud 00aAn Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers0 aExistence and Uniqueness Result for the Motion of SelfPropelled bSociety for Industrial and Applied Mathematics a1345-13680 v 433 aWe present an analytical framework to study the motion of micro-swimmers in a viscous fluid. Our main result is that, under very mild regularity assumptions, the change of shape determines uniquely the motion of the swimmer. We assume that the Reynolds number is very small, so that the velocity field of the surrounding, infinite fluid is governed by the Stokes system and all inertial effects can be neglected. Moreover, we enforce the self propulsion constraint (no external forces and torques). Therefore, Newton\\\'s equations of motion reduce to the vanishing of the viscous drag force and torque acting on the body. By exploiting an integral representation of viscous force and torque, the equations of motion can be reduced to a system of six ordinary differential equations. Variational techniques are used to prove the boundedness and measurability of its coefficients, so that classical results on ordinary differential equations can be invoked to prove existence and uniqueness of the solution.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMorandotti, Marco uhttp://hdl.handle.net/1963/389401004nas a2200133 4500008004100000245007400041210006900115260003400184520055100218653001800769100002100787700002600808856003600834 2011 en d00aExistence for wave equations on domains with arbitrary growing cracks0 aExistence for wave equations on domains with arbitrary growing c bEuropean Mathematical Society3 aIn this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.10aWave equation1 aDal Maso, Gianni1 aLarsen, Cristopher J. uhttp://hdl.handle.net/1963/428400336nas a2200109 4500008004100000245004800041210004700089260001000136100002100146700002300167856003600190 1999 en d00aEvans-Vasilesco theorem in Dirichlet spaces0 aEvansVasilesco theorem in Dirichlet spaces bSISSA1 aDal Maso, Gianni1 aDe Cicco, Virginia uhttp://hdl.handle.net/1963/6436