The paper establishes well-posedness and semigroup generation for a linear
dynamic plate equation with non-monotone boundary conditions. The lack of
dissipation prevents applicability of the classical semigroup theory,
approximation techniques, or energy methods. Investigation of such systems was
originally motivated by applications, but due to the challenging nature of the
problem had been essentially limited to 1-dimensional models. A more recent
result [BeLa], though still dealing with a (1D) Euler-Bernoulli beam, showed how
the wellposedness in absence of dissipativity can be approached using tools of
microlocal analysis, potentially applicable in higher dimensions. This paper
extends the later work to a two dimensional system. The main difficulties in the
2D setting arise from a substantially increased complexity of boundary
operators, and the failure of the uniform Lopatinskii condition, which
ultimately necessitates additional control on tangential components of the
boundary traces. The latter issue is handled by introducing a suitably
constructed boundary feedback which acts as the additional moment present on the
boundary of the two-dimensional domain.