Abstract
Abstract The paper studies the existence of global strong attractor for the Kirchhoff type 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 ) . It proves that in strictly positive stiffness factors and supercritical nonlinearity case, there exists a global finite-dimensional attractor in the natural energy space endowed with strong topology (rather than partially strong topology). The result extends the recent one achieved by Chueshov (2012).
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