Year-end Sale % OFF 
Abstract
We consider a degenerate equation with a memory condition at the boundary. For a wider class of relaxation functions, we establish a more general decay result, from which the usual exponential and polynomial decay rates are only special cases.
Highlights
The main purpose of this paper is to investigate the asymptotic behavior of the solutions of the degenerate equation with a memory condition at the boundaryK (x) u + Δ2u + f (u) = 0 in Q = Ω × (0, ∞), (1) u = ∂u ∂] on Γ0 × (0, ∞), (2) t−u + ∫ g1 (t − s) B2u (s) ds = 0 on Γ1 × (0, ∞), (3) + ∫
If we denote the compactness of Γ1 by m(x) = x − x0, condition (12) implies that there exists a small positive constant δ0 such that 0 < δ0 ≤ m(x) ⋅ ](x), for all x ∈ Γ1
The following lemma states an important property of the convolution operator
Summary
Cavalcanti et al [19] proved the uniform decay rates of solutions to a degenerate system with a memory condition at the boundary. Park and Kang [22] studied the exponential decay for the Kirchhoff plate equations with nonlinear dissipation and boundary memory condition. They proved that the energy decays uniformly exponentially or algebraically with the same rate of decay as the relaxation functions. Messaoudi and Soufyane [23], Mustafa and Messaoudi [24], and Santos and Soufyane [25] proved the general decay for the wave equation, Timoshenko system, and von Karman plate system with viscoelastic boundary conditions, respectively.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
