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GLOBAL EXISTENCE OF WEAK SOLUTIONS FOR STRONGLY DAMPED WAVE EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS AND BALANCED POTENTIALS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 99 / Issue 3 / June 2019
- Published online by Cambridge University Press:
- 07 February 2019, pp. 432-444
- Print publication:
- June 2019
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- Article
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We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. The associated linear operator is
$(-\unicode[STIX]{x1D6E5}_{W})^{\unicode[STIX]{x1D703}}\unicode[STIX]{x2202}_{t}u$, where 
$\unicode[STIX]{x1D703}\in [\frac{1}{2},1)$ and 
$\unicode[STIX]{x1D6E5}_{W}$ is the Wentzell–Laplacian. 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 of each potential, as well as mixed dissipative/antidissipative behaviour.
