Regular solutions and strong attractors for the Kirchhoff wave model with structural nonlinear damping Abstract   The paper investigates the regular solutions and the strong global and exponential attractors for the Kirchhoff wave model with structural nonlinear damping       u    t  t    xe2x88x92  xcfx95   (    xe2x80x96  xe2x88x87  u  xe2x80x96    2    )   xcex94  u    xcfx83   (    xe2x80x96  xe2x88x87  u  xe2x80x96    2    )      (  xe2x88x92  xcex94  )     xcexb8      u    t      f   (  u  )     g   (  x  )     , with     xcexb8  xe2x88x88     1  xe2x88x95  2  ,  1  )     . It shows that under the same assumptions as in Li and Yang (2019), the weak solution obtained in Li and Yang (2019) is exactly the strong one, and the global and exponential attractor obtained there are exactly the strong ones in the strong solution space. These results improve and deepen those in Li and Yang (2019).

Boundary state feedback exponential stabilization for a onedimensional wave equation with velocity recirculation Abstract   In this paper, we consider boundary state feedback stabilization of a onedimensional wave equation with indomain feedbackrecirculation of an intermediate point velocity. We firstly construct an auxiliary control system which has a nonlocal term of the displacement at the same intermediate point. Then by choosing a wellknown exponentially stable wave equation as its target system, we find one backstepping transformation from which a state feedback law for this auxiliary system is proposed. Finally, taking the resulting closedloop of the auxiliary system as a new target system, we obtain another backstepping transformation from which a boundary state feedback controller for the original system is designed. By the equivalence of three systems, the closedloop of original system is proved to be wellposed and exponentially stable. Some numerical simulations are presented to validate the theoretical results.