Asymptotic behavior of solutions for the time-delayed equations of Benjamin-Bona-Mahony’s type

Abstract

In this paper, we investigate the asymptotic behavior of the solutions for the equations of Benjamin-Bona-Mahony's type with a time delay. We prove the global existence of solutions and energy decay. By using the Liapunov function method, we shall show that the solution is exponentially decay if the delay parameter τ is sufficiently small. MSC: 35R10; 35B35; 35Q53

Asymptotic behavior of the linearized compressible barotropic Navier‐Stokes system with a time varying delay term in the boundary or internal feedback

“…For semilinear wave type equation, see [35]; for nonlinear wave equation with switching delay, see [28]. In the constant time delay case, we refer to the other related works: [36] for Schrodinger equation, [37] for KdV equation with boundary time-delay, [38] for KdV equation with interior delay feedback, [39] KdV equation with star shaped network, [40][41][42] for Kawahara equation with boundary and interior time delay feedback, respectively, [43] for KdV-Burger equation, Kuramoto-Sivashinsky equation with the time delay in the nonlinear term [44], Benjamin-Bona-Mahony equation [45], and microbeam equation [46], and for other evolution equation with time delay feedback, see [47].…”