We demonstrate the global existence of weak solutions to a class of
semilinear strongly damped wave equations possessing nonlinear hyperbolic
dynamic boundary conditions. Our work assumes (βΞWβ)ΞΈβtβu
with ΞΈβ[21β,1) and where ΞWβ is the Wentzell-Laplacian.
Hence, the associated linear operator admits a compact resolvent. A balance
condition is assumed to hold between the nonlinearity defined on the interior
of the domain and the nonlinearity on the boundary. This allows for arbitrary
(supercritical) polynomial growth on each potential, as well as mixed
dissipative/anti-dissipative behavior. Moreover, the nonlinear function defined
on the interior of the domain is assumed to be only C0