Existence and asymptotic behavior of global smooth solution for p -system with nonlinear damping and fixed boundary effect

2013 ◽  
Vol 37 (17) ◽  
pp. 2585-2596 ◽  
Author(s):  
Mina Jiang ◽  
Yinghui Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Smooth Solution ◽  
Boundary Effect ◽  
Nonlinear Damping ◽  
P System ◽  
Fixed Boundary ◽  
Global Smooth Solution

Existence of a global smooth solution to the initial boundary-value problem for the p-system with nonlinear damping

2013 ◽  
Vol 143 (6) ◽  
pp. 1243-1253
Author(s):  
Mina Jiang ◽  
Dong Li ◽  
Lizhi Ruan
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Smooth Solution ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
P System ◽  
Global Smooth Solution ◽  
Initial Boundary Value

This paper is concerned with the initial boundary-value problem for the p-system with nonlinear damping. We prove the existence of a global smooth solution under the assumption that only the C0-norm of the derivative of the initial data is sufficiently small, while the C0-norm of the initial data is not necessarily small. The proof is based on several key a priori estimates, the maximum principle and the characteristic method.

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 Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Huimin Yu
Keyword(s):  
Asymptotic Behavior ◽  
Euler Equations ◽  
Boundary Effect ◽  
Nonlinear Damping ◽  
Compressible Euler Equations ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Slip Boundary ◽  
Compressible Euler ◽  
Linear Damping

The asymptotic behavior (as well as the global existence) of classical solutions to the 3D compressible Euler equations are considered. For polytropic perfect gas(P(ρ)=P0ργ), time asymptotically, it has been proved by Pan and Zhao (2009) that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy's law. In this paper, we use a more general method and extend this result to the 3D compressible Euler equations with nonlinear damping and a more general pressure term. Comparing with linear damping, nonlinear damping can be ignored under small initial data.

Global Existence and Asymptotic Behavior of Solutions for Nonlinear Wave Equations

2014 ◽  
Vol 490-491 ◽  
pp. 327-330
Author(s):  
Ji Bing Zhang ◽  
Yun Zhu Gao
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Damping ◽  
Nonlinear Wave Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Source Terms ◽  
Damping And Source Terms

In this paper, we concern with the nonlinear wave equations with nonlinear damping and source terms. By using the potential well method, we obtain a result for the global existence and asymptotic behavior of the solutions.

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