In this poster we shall consider a wave model in 3D on a bounded domain which contains nonlinear sources with critical exponent in the interior/boundary and nonlinear feedback dissipation on the boundary. Similar models with simpler nonlinear boundary terms have been already studied broadly whereas the generality of our model is not only the presence of nonlinear interior and boundary damping but also nonlinear boundary source. Boundary actuators are easily accessible to external manipulations-hence feasible from the engineering point of view and practically implementable. On the other hand, the underlying mathematics is challenging. Boundary actions are represented by unbounded, unclosable operators, hence not treatable by perturbation theory(even from the point of view of well-posedness theory.) Our main result shows that a suitably calibrated boundary damping prevents the blow up of the waves, and allows to contain wave asymptotically (in time) in a suitable attracting set which is compact.
Global attractors for a wave equation subject to nonlinear boundary dissipation and nonlinear interior/boundary sources with critical exponents.
MADHUMITA ROY, GA, University of MemphisAuthors: Jose H. Rodrigues and Madhumita Roy
2022 AWM Research Symposium