Abstract
We consider abstract nonlinear second-order-in-time systems with damping. The nonlinearity is assumed to satisfy a monotonicity condition as well as certain smoothness conditions. Well posedness of solutions is established and several examples of interest are discussed. A nonlinear variation-of-parameters representation for solutions in terms of an associated linear semigroup is also given.
Citation
H. T. Banks. David S. Gilliam. Victor I. Shubov. "Global solvability for damped abstract nonlinear hyperbolic systems." Differential Integral Equations 10 (2) 309 - 332, 1997. https://doi.org/10.57262/die/1367526340
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