Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction
We establish, subject to some natural additional assumptions imposed on the relation between the source and the damping, both well-posedness and effective optimal decay rates for the solutions of a semilinear model of the wave equation. The theory presented allows to consider both superlinear and sublinear behaviours of the dissipation in the presence of unstructured sources. © 2007 Elsevier Inc. All rights reserved.
Journal of Differential Equations
Cavalcanti, M., Domingos Cavalcanti, V., & Lasiecka, I. (2007). Well-posedness and optimal decay rates for the wave equation with nonlinear boundary damping-source interaction. Journal of Differential Equations, 236 (2), 407-459. https://doi.org/10.1016/j.jde.2007.02.004