scholarly journals Global solutions of wave equations with multiple nonlinear source terms under acoustic boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shoubo Jin ◽  
Jian Li
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Wave Equations ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Functional ◽  
Source Terms ◽  
Acoustic Boundary Conditions ◽  
Nonlinear Source

AbstractUnder the acoustic boundary conditions, the initial boundary value problem of a wave equation with multiple nonlinear source terms is considered. This paper gives the energy functional of regular solutions for the wave equation and proves the decreasing property of the energy functional. Firstly, the existence of a global solution for the wave equation is proved by the Faedo–Galerkin method. Then, in order to obtain the nonexistence of global solutions for the wave equation, a new functional is defined. When the initial energy is less than zero, the special properties of the new functional are proved by the method of contraction. Finally, the conditions for the nonexistence of global solutions of the wave equation with acoustic boundary conditions are analyzed by using these special properties.

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.

scholarly journals Global solutions and general decay for the dispersive wave equation with memory and source terms

2020 ◽  
Vol 4 (2) ◽  
pp. 116-122
Author(s):  
Mohamed Mellah ◽  
Keyword(s):  
Wave Equation ◽  
Global Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
General Decay ◽  
Dispersive Wave ◽  
Source Terms ◽  
Initial Boundary Value ◽  
With Memory ◽  
Dispersive Wave Equation

This paper concerns with the global solutions and general decay to an initial-boundary value problem of the dispersive wave equation with memory and source terms

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.

ON BOUNDARY CONDITIONS FOR FIRST-ORDER SYMMETRIC HYPERBOLIC SYSTEMS WITH CONSTRAINTS

2013 ◽  
Vol 10 (04) ◽  
pp. 725-734 ◽  
Author(s):  
NICOLAE TARFULEA
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Hyperbolic Systems ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
First Order ◽  
The Cauchy Problem ◽  
Initial Boundary Value ◽  
Well Posed

The Cauchy problem for many first-order symmetric hyperbolic (FOSH) systems is constraint preserving, i.e. the solution satisfies certain spatial differential constraints whenever the initial data does. Frequently, artificial space cut-offs are performed for such evolution systems, usually out of the necessity for finite computational domains. However, it may easily happen that boundary conditions at the artificial boundary for such a system lead to an initial boundary value problem which, while well-posed, does not preserve the constraints. Here we consider the problem of finding constraint-preserving boundary conditions for constrained FOSH systems in the well-posed class of maximal non-negative boundary conditions. Based on a characterization of maximal non-negative boundary conditions, we discuss a systematic technique for finding such boundary conditions that preserve the constraints, pending that the constraints satisfy a FOSH system themselves. We exemplify this technique by analyzing a system of wave equations in a first-order formulation subject to divergence constraints.

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.

scholarly journals Blow-Up for a Stochastic Viscoelastic Lamé Equation with Logarithmic Nonlinearity

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Amina Benramdane ◽  
Nadia Mezouar ◽  
Mohammed Sulaiman Alqawba ◽  
Salah Mahmoud Boulaaras ◽  
Bahri Belkacem Cherif
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Blow Up ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Damping ◽  
Nonlinear Source ◽  
Viscoelastic Wave ◽  
Initial Boundary Value

In this paper, we consider an initial boundary value problem of stochastic viscoelastic wave equation with nonlinear damping and logarithmic nonlinear source terms. We proved a blow-up result for the solution with decreasing kernel.

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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