Abstract
We study the existence of exponential attractor for the Kirchhoff equations with strong nonlinear damping and supercritical nonlinearity u t t − σ ( ‖ ∇ u ‖ 2 ) Δ u t − ϕ ( ‖ ∇ u ‖ 2 ) Δ u + f ( u ) = h ( x ) . The main result is that the nonlinearity f ( u ) is of supercritical growth. In this case we establish an exponential attractor in natural energy space by using a new method based on the weak quasi-stability estimates (rather than the strong one as usual).
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