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.

%B Journal of Differential Equations %V 261 %P 4897 - 4923 %G eng %U http://www.sciencedirect.com/science/article/pii/S0022039616301772 %R https://doi.org/10.1016/j.jde.2016.07.012 %0 Report %D 2015 %T Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition %A Gianni Dal Maso %A Cristopher J. Larsen %A Rodica Toader %X 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. %G en %U http://urania.sissa.it/xmlui/handle/1963/35045 %1 35277 %2 Mathematics %4 1 %# MAT/05 %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2015-11-18T15:46:32Z No. of bitstreams: 1 DM-Lar-Toa-SISSA.pdf: 313034 bytes, checksum: 76419fd2c8c435ae7deeca773b424667 (MD5) %0 Journal Article %D 2014 %T Editorial %A Ciro Ciliberto %A Gianni Dal Maso %A Pasquale Vetro %I Springer %G en %U http://urania.sissa.it/xmlui/handle/1963/34712 %1 34926 %2 Mathematics %4 1 %$ Approved for entry into archive by Maria Pia Calandra (calapia@sissa.it) on 2015-10-26T10:50:12Z (GMT) No. of bitstreams: 0 %R 10.1007/s12215-014-0172-8 %0 Journal Article %J Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %D 2011 %T Ennio De Giorgi and Γ-convergence %A Gianni Dal Maso %X 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. %B Discrete and Continuous Dynamical Systems - Series A 31 (2011) 1017-1021 %I American Institute of Mathematical Sciences %G en %U http://hdl.handle.net/1963/5308 %1 5138 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2012-01-31T12:04:34Z\\nNo. of bitstreams: 0 %R 10.3934/dcds.2011.31.1017 %0 Journal Article %J SIAM J. Math. Anal. %D 2011 %T An Existence and Uniqueness Result for the Motion of Self-Propelled Microswimmers %A Gianni Dal Maso %A Antonio DeSimone %A Marco Morandotti %XWe 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.

%B SIAM J. Math. Anal. %I Society for Industrial and Applied Mathematics %V 43 %P 1345-1368 %G en_US %U http://hdl.handle.net/1963/3894 %1 815 %2 Mathematics %3 Functional Analysis and Applications %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2010-07-23T11:44:06Z\\r\\nNo. of bitstreams: 1\\r\\nMorandotti_44M.pdf: 217358 bytes, checksum: 4c362016bb2220e7a97805254b7fb870 (MD5) %R 10.1137/10080083X %0 Journal Article %J Rend. Lincei Mat. Appl. 22 (2011) 387-408 %D 2011 %T Existence for wave equations on domains with arbitrary growing cracks %A Gianni Dal Maso %A Cristopher J. Larsen %K Wave equation %X 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. %B Rend. Lincei Mat. Appl. 22 (2011) 387-408 %I European Mathematical Society %G en %U http://hdl.handle.net/1963/4284 %1 4015 %2 Mathematics %3 Functional Analysis and Applications %4 -1 %$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2011-09-27T09:09:30Z\\r\\nNo. of bitstreams: 1\\r\\nDM-Lar_32_M.pdf: 223891 bytes, checksum: 7c6c66b6d21936b33ed0c21574928e24 (MD5) %R 10.4171/RLM/606 %0 Journal Article %J Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %D 1999 %T Evans-Vasilesco theorem in Dirichlet spaces %A Gianni Dal Maso %A Virginia De Cicco %B Rendiconti di Matematica e delle sue Applicazioni. vol. 19, Issue 7, (1999), pages : 1-15 %I SISSA %G en %U http://hdl.handle.net/1963/6436 %1 6376 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Gianni Dal Maso (dalmaso@sissa.it) on 2013-01-31T18:39:11Z\\nNo. of bitstreams: 2\\nDM-DeC-96.pdf: 145467 bytes, checksum: 0cf974ac5cc090ff7f9faae3d433043f (MD5)\\nDM-DeC-96-cover.pdf: 35849 bytes, checksum: cde85af897042e1ee2c1b1a8c724b8eb (MD5)