Markus Schöberl, Kurt Schlacher,
"Port?Hamiltonian representation for pdes with second?order derivatives in the energy density"
: Proceedings in Applied Mathematics and Mechanics (PAMM), Serie Proceedings in Applied Mathematics and Mecha, Vol. 16, Nummer 1, WILEY?VCH Verlag, Seite(n) 19-22, 10-2016
Port?Hamiltonian representation for pdes with second?order derivatives in the energy density
Sprache des Titels:
Proceedings in Applied Mathematics and Mechanics (PAMM)
In this contribution we consider a port-Hamiltonian setting for partial differential equations. A crucial property of this system
class is the property to be able to link a power balance relation to the structure of the equations. However, one has to take into
account also the effects of energy flows via the boundary. This is straightforward when the Hamiltonian depends on derivative
variables of first order, e.g. by using integration by parts. If second-order derivatives appear then integration by parts cannot
be used without due care, thus we suggest an approach by using the so-called Cartan-form. We visualize the derivation of a
power balance relation by using the Kirchhoff plate as an example.