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.

VL - 261 UR - http://www.sciencedirect.com/science/article/pii/S0022039616301772 ER - TY - RPRT T1 - Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2015 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - There 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. UR - http://urania.sissa.it/xmlui/handle/1963/35045 U1 - 35277 U2 - Mathematics U4 - 1 U5 - MAT/05 ER - TY - JOUR T1 - Editorial Y1 - 2014 A1 - Ciro Ciliberto A1 - Gianni Dal Maso A1 - Pasquale Vetro PB - Springer UR - http://urania.sissa.it/xmlui/handle/1963/34712 U1 - 34926 U2 - Mathematics U4 - 1 ER - TY - JOUR T1 - Ennio De Giorgi and Γ-convergence JF - Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 Y1 - 2011 A1 - Gianni Dal Maso AB - Γ-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. PB - American Institute of Mathematical Sciences UR - http://hdl.handle.net/1963/5308 U1 - 5138 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers JF - SIAM J. Math. Anal. Y1 - 2011 A1 - Gianni Dal Maso A1 - Antonio DeSimone A1 - Marco Morandotti AB -We 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.

PB - Society for Industrial and Applied Mathematics VL - 43 UR - http://hdl.handle.net/1963/3894 U1 - 815 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Existence for wave equations on domains with arbitrary growing cracks JF - Rend. Lincei Mat. Appl. 22 (2011) 387-408 Y1 - 2011 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen KW - Wave equation AB - In 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. PB - European Mathematical Society UR - http://hdl.handle.net/1963/4284 U1 - 4015 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER - TY - JOUR T1 - Evans-Vasilesco theorem in Dirichlet spaces JF - Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 Y1 - 1999 A1 - Gianni Dal Maso A1 - Virginia De Cicco PB - SISSA UR - http://hdl.handle.net/1963/6436 U1 - 6376 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER -