Longtime behavior of the Kirchhoff type equation with strong damping on RN

By Zhijian Yang. 2007

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Abstract The paper studies the longtime behavior of the Kirchhoff type equation with strong damping on R N : u t t − M ( ‖ ∇ u ‖ 2 ) Δ u − Δ u t + u + u t + g ( x , u ) = f ( x ) . It shows that the related continuous semigroup S ( t ) possesses a global attractor which is connected and has finite fractal and Hausdorff dimension.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/beeeaeec14b9c29bc882dc2b6339de7b60555c81