Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent (Q928445)

The paper addresses long-time behavior of solutions to the semilinear wave equation \(w_{tt}-\Delta w+\chi (x)g(w_{t})=f(w)\) satisfying initial data and Dirichlet or Dirichlet-Neumann or Neumann-Robin boundary conditions. The authors establish finite-dimensionality and smoothness of global attractors associated with finite energy solution to the above equation with the source \(f\) of critical exponent.