Decay rate of the range component of solutions to some semilinear evolution equations

@article{Haraux2006DecayRO,
  title={Decay rate of the range component of solutions to some semilinear evolution equations},
  author={Alain Haraux},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  year={2006},
  volume={13},
  pages={435-445}
}
Abstract.We examine the rate of decay to 0, as t → +∞., of the projection on the range of A of the solutions of an equation of the form u′ + Au + |u|p−1u = 0 or u′′ + u′ + Au + |u|p−1u = 0 in a bounded domain of $$\mathbb {R}$$ N, where A = −Δ with Neumann boundary conditions or A = −Δ − λ1I with Dirichlet boundary conditions. In general this decay is much faster than the decay of the projection on the kernel; it is often exponential, but apparently not always.