# 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.

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