scholarly journals Viscoelasticity with time-dependent memory kernels, II: asymptotic behavior of solutions

2018 ◽  
Vol 140 (6) ◽  
pp. 1687-1729
Author(s):  
Monica Conti ◽  
Valeria Danese ◽  
Vittorino Pata
Keyword(s):  
Asymptotic Behavior ◽  
Time Dependent ◽  
Asymptotic Behavior Of Solutions

scholarly journals Boundary Effect on Asymptotic Behavior of Solutions to the p-System with Time-Dependent Damping

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Ran Duan ◽  
Mina Jiang ◽  
Yinghui Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Dirichlet Boundary ◽  
Boundary Effect ◽  
Initial Perturbation ◽  
Time Dependent ◽  
Asymptotic Behavior Of Solutions ◽  
P System ◽  
Weighted Energy Method ◽  
Weighted Energy ◽  
Constant State

In this paper, we consider the asymptotic behavior of solutions to the p-system with time-dependent damping on the half-line R+=0,+∞, vt−ux=0,ut+pvx=−α/1+tλu with the Dirichlet boundary condition ux=0=0, in particular, including the constant and nonconstant coefficient damping. The initial data v0,u0x have the constant state v+,u+ at x=+∞. We prove that the solutions time-asymptotically converge to v+,0 as t tends to infinity. Compared with previous results about the p-system with constant coefficient damping, we obtain a general result when the initial perturbation belongs to H3R+×H2R+. Our proof is based on the time-weighted energy method.

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