scholarly journals Sharp time decay rates on a hyperbolic plate model under effects of an intermediate damping with a time-dependent coefficient

2015 ◽  
Vol 36 (5) ◽  
pp. 2419-2447 ◽  
Author(s):  
Cleverson Roberto da Luz ◽  
Ruy Coimbra Charão ◽  
Marcello D'Abbicco
Keyword(s):  
Decay Rates ◽  
Time Dependent ◽  
Time Decay ◽  
Plate Model ◽  
Time Decay Rates

STABILITY OF SHOCK PROFILES FOR NONCONVEX SCALAR VISCOUS CONSERVATION LAWS

1995 ◽  
Vol 05 (03) ◽  
pp. 279-296 ◽  
Author(s):  
MING MEI
Keyword(s):  
Conservation Laws ◽  
Decay Rates ◽  
Asymptotically Stable ◽  
Time Decay ◽  
Shock Condition ◽  
Viscous Conservation Laws ◽  
Time Decay Rates ◽  
Shock Profiles ◽  
Degenerate Shock ◽  
The Stability

This paper is to study the stability of shock profiles for nonconvex scalar viscous conservation laws with the nondegenerate and the degenerate shock conditions by means of an elementary energy method. In both cases, the shock profiles are proved to be asymptotically stable for suitably small initial disturbances. Moreover, in the case of nondegenerate shock condition, time decay rates of asymptotics are also obtained.

scholarly journals Time decay rates for the compressible viscoelastic flows

2017 ◽  
Vol 452 (2) ◽  
pp. 990-1004 ◽  
Author(s):  
Guochun Wu ◽  
Zhensheng Gao ◽  
Zhong Tan
Keyword(s):  
Decay Rates ◽  
Viscoelastic Flows ◽  
Time Decay ◽  
Time Decay Rates

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

2021 ◽  
pp. 1-34
Author(s):  
Yuhui Chen ◽  
Minling Li ◽  
Qinghe Yao ◽  
Zheng-an Yao
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Convergence Rates ◽  
Splitting Method ◽  
Mhd Flow ◽  
Decay Rates ◽  
Upper And Lower Bounds ◽  
Time Decay ◽  
Large Solutions ◽  
Time Decay Rates

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p ( R 2 ) ∩ L 2 ( R 2 ). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized.

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