TY - JOUR
T1 - The time-dependent von Kármán plate equation as a limit of 3d nonlinear elasticity
JF - Calculus of Variations and Partial Differential Equations 41 (2011) 241-259
Y1 - 2011
A1 - Helmut Abels
A1 - Maria Giovanna Mora
A1 - Stefan Müller
AB - The asymptotic behaviour of the solutions of three-dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness $h$ of the plate tends to zero. Under appropriate scalings of the applied force and of the initial values in terms of $h$, it is shown that three-dimensional solutions of the nonlinear elastodynamic equation converge to solutions of the time-dependent von K\\\\\\\'arm\\\\\\\'an plate equation.
PB - Springer
UR - http://hdl.handle.net/1963/3835
U1 - 492
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - RPRT
T1 - Time-dependent systems of generalized Young measures
Y1 - 2007
A1 - Gianni Dal Maso
A1 - Antonio DeSimone
A1 - Maria Giovanna Mora
A1 - Massimiliano Morini
AB - In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.
JF - Netw. Heterog. Media 2 (2007) 1-36
UR - http://hdl.handle.net/1963/1795
U1 - 2749
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -