scholarly journals Time-weighted energy method for quasi-linear hyperbolic systems of viscoelasticity

2011 ◽  
Vol 87 (6) ◽  
pp. 99-102 ◽  
Author(s):  
Priyanjana M. N. Dharmawardane ◽  
Tohru Nakamura ◽  
Shuichi Kawashima
Keyword(s):  
Energy Method ◽  
Hyperbolic Systems ◽  
Weighted Energy Method ◽  
Weighted Energy

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.

scholarly journals General stability and exponential growth of nonlinear variable coefficient wave equation with logarithmic source and memory term

2021 ◽  
Author(s):  
Long Yan ◽  
Lili Sun
Keyword(s):  
Wave Equation ◽  
Asymptotic Stability ◽  
Exponential Growth ◽  
Variable Coefficient ◽  
Nonlinear Damping ◽  
Memory Term ◽  
Weighted Energy Method ◽  
Weighted Energy ◽  
General Stability ◽  
Stability And Instability

This paper is concerned with the asymptotic stability and instability of solutions to a variable coefficient logarithmic wave equation with nonlinear damping and memory term. This model describes wave travelling through nonhomogeneous viscoelastic materials. By choosing appropriate multiplier and using weighted energy method, we prove the exponential decay of the energy. Besides, we also obtain the instability at the infinity of the solutions in the presence of the nonlinear damping.

scholarly journals Global stability of traveling wave fronts in a two-dimensional lattice dynamical system with global interaction

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Cui-Ping Cheng ◽  
Ruo-Fan An
Keyword(s):  
Dynamical System ◽  
Traveling Wave ◽  
Single Species ◽  
Wave Fronts ◽  
Dimensional Lattice ◽  
Weighted Energy Method ◽  
Traveling Wave Fronts ◽  
Weighted Energy ◽  
Lattice Dynamical System ◽  
Exponentially Stable

<p style='text-indent:20px;'>This paper is concerned with the traveling wave fronts for a lattice dynamical system with global interaction, which arises in a single species in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay. We prove that all non-critical traveling wave fronts are globally exponentially stable in time, and the critical traveling wave fronts are globally algebraically stable by the weighted energy method combined with the comparison principle and the discrete Fourier transform.</p>

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