Global asymptotic behavior of solutions to a class of Kirchhoff equations

Abstract

In this paper, a parabolic type Kirchhoff equation and its stationary counterpart are considered. For the evolution problem, the precise decay rates of the weak solution and of the corresponding energy functional are derived. For the stationary problem, a ground-state solution is obtained by applying Lagrange multiplier method. Moreover, the asymptotic behaviors of the general global solutions are also described. These results extend some recent ones obtained in [Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy, Computers and Mathematics with Applications, 75(2018), 3283-3297] by Han and Li.