scholarly journals Global Existence and Asymptotic Behavior of Solutions for a Class of Nonlinear Degenerate Wave Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun Ye
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equations ◽  
Decay Estimate ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Potential Well ◽  
Initial Boundary Value ◽  
Nonlinear Degenerate

This paper studies the existence of global solutions to the initial-boundary value problem for some nonlinear degenerate wave equations by means of compactness method and the potential well idea. Meanwhile, we investigate the decay estimate of the energy of the global solutions to this problem by using a difference inequality.

scholarly journals Existence and Decay Estimate of Global Solutions to Systems of Nonlinear Wave Equations with Damping and Source Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun Ye
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Decay Estimate ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Wave Equations ◽  
Stable Set ◽  
Initial Boundary Value ◽  
Damping And Source Terms

The initial-boundary value problem for a class of nonlinear wave equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set and obtain the asymptotic stability of global solutions through the use of a difference inequality.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS FOR A 1D ISOTHERMAL VISCOUS GAS

2008 ◽  
Vol 18 (08) ◽  
pp. 1383-1408 ◽  
Author(s):  
YUMING QIN ◽  
YANLI ZHAO
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Stokes Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Asymptotic Behavior Of Solutions ◽  
Navier Stokes Equations ◽  
Viscous Gas ◽  
Initial Boundary Value

In this paper, we prove the global existence and asymptotic behavior of solutions in Hi(i = 1, 2) to an initial boundary value problem of a 1D isentropic, isothermal and the compressible viscous gas with an non-autonomous external force in a bounded region.

Energy Decay of Global Solutions for a System of Petrovsky Equations

2013 ◽  
Vol 405-408 ◽  
pp. 3160-3164
Author(s):  
Yao Jun Ye
Keyword(s):  
Boundary Value Problem ◽  
Bounded Domain ◽  
Decay Estimate ◽  
Boundary Value ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Decay ◽  
Difference Inequality ◽  
Initial Boundary Value

The initial-boundary value problem for a class of nonlinear Petrovsky systems in bounded domain is studied. We prove the energy decay estimate of global solutions through the use of a difference inequality.

Non-existence of global solutions for a class of wave equations with nonlinear damping and source terms

2011 ◽  
Vol 141 (4) ◽  
pp. 865-880 ◽  
Author(s):  
Shun-Tang Wu
Keyword(s):  
Wave Equations ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Critical Value ◽  
Initial Energy ◽  
Source Terms ◽  
Initial Boundary Value ◽  
Damping And Source Terms

An initial–boundary-value problem for a class of wave equations with nonlinear damping and source terms in a bounded domain is considered. We establish the non-existence result of global solutions with the initial energy controlled above by a critical value via the method introduced in a work by Autuori et al. in 2010. This improves the 2009 result of Liu and Wang.

Asymptotic Behavior of Global Solutions for some Nonlinear Wave Equation

2014 ◽  
Vol 638-640 ◽  
pp. 1691-1694
Author(s):  
Yong Xian Yan
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Boundary Value Problem ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Damping Term ◽  
Initial Boundary Value

In this paper we study the asymptotic behavior of the global solutions to the initial-boundary value problem of the nonlinear wave equation with damping term by applying a difference inequality.

Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation

1980 ◽  
Vol 32 (3) ◽  
pp. 631-643 ◽  
Author(s):  
G. F. Webb
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Ordinary Differential Equation ◽  
Asymptotic Behavior ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Bounded Domain ◽  
Initial Boundary Value ◽  
Strongly Damped

In this paper we study the nonlinear initial boundary value problem(1.1) ωtt— αΔ ωt— Δω= f(ω), t> 0ω(x, 0) = ϕ(x), x∈ Ωωt(x, 0) = ψ (x), x∈ Ωω(x, t ) = 0, x ∈ ∂Ω, t ≥ 0.In (1.1) Ω is a smooth bounded domain in Rn, n = 1, 2, 3, α > 0, and f ∈ C1(R;R) with f‘(x) ≦ co for all x ∈ R (where c0 is a nonnegative constant), lim sup|x|→+∞f(x)/x ≦0, and f(0) = 0. Our objective will be to establish the existence of unique strong global solutions to (1.1) and investigate their behavior as t→ +∞.Our approach takes advantage of the semilinear character of (1.1) and reformulates the problem as an abstract ordinary differential equation in a Banach space.

Asymptotic Behavior of Solution for Higher-Order Wave Equation

2013 ◽  
Vol 411-414 ◽  
pp. 1419-1422
Author(s):  
Wan Zhen Zhu ◽  
Yao Jun Ye
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Asymptotic Stability ◽  
Boundary Value Problem ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Initial Boundary Value ◽  
Damping And Source Terms

In this paper the asymptotic stability of global solutions to the initial-boundary value problem for some nonlinear wave equation with nonlinear damping and source terms is studied by using a difference ineauality.

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