Appl Math Optim 54:117–130 (2006)
2006 Springer Science+Business Media, Inc.
Viscosity Solution of the Hamilton–Jacobi Equation
Arising from a Thin Film Blistering Model
and Giorgio Vergara Caffarelli
Istituto per le Applicazioni del Calcolo “M. Picone”,
V. Policlinico 137, 00161 Roma, Italy
Dipartimento MeMoMat, Universit`a di Roma “La Sapienza”,
V. A. Scarpa 16, 00161 Roma, Italy
Abstract. The paper deals with a dynamical nonlinear model describing the self-
driven delamination of compressed thin ﬁlms. Some assumptions on the buckled
shape allow us to describe the moving boundary of the ﬁlm by a single Hamilton–
Jacobi equation. We prove the existence and uniqueness of a viscosity solution to
the associated evolution problem.
Key Words. Thin ﬁlm delamination, Viscosity solution.
AMS Classiﬁcation. 35DXX, 74KXX.
In several ﬁlm/substrate systems, the ﬁlm is in a state of residual compression; this
compression, observed especially in thin ﬁlms which have been sprayed, can create the
formation of small blisters in some regions where the cohesion ﬁlm/substrate is weaker
or imperfect. As a consequence of the stresses on the interfacial fracture, the damage
spreads assuming even funny shapes.
This work was partially supported by the European Community’s Human Potential Programme under
Contract HPRN-CT-2002-00284 SMART-SYSTEMS and the CNR/MIUR project “Materiali Compositi per
Applicazioni Strutturali di Rilevante Interesse Industriale”.