Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation

2015 ◽  
Vol 13 (03) ◽  
pp. 233-254 ◽  
Author(s):  
Shuichi Kawashima ◽  
Yu-Zhu Wang
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Dispersion Equation ◽  
Dimensional Space ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Linear Solution ◽  
Asymptotic Decay ◽  
Decay Of Solutions ◽  
Double Dispersion

In this paper, we study the initial value problem for the generalized cubic double dispersion equation in n-dimensional space. Under a small condition on the initial data, we prove the global existence and asymptotic decay of solutions for all space dimensions n ≥ 1. Moreover, when n ≥ 2, we show that the solution can be approximated by the linear solution as time tends to infinity.

scholarly journals Global Existence and Asymptotic Behavior of Solutions to the Generalized Damped Boussinesq Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Yinxia Wang ◽  
Hengjun Zhao
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Global Existence ◽  
Decay Estimate ◽  
Boussinesq Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
Linear Solution ◽  
Optimal Decay ◽  
The Cauchy Problem

We investigate the Cauchy problem for the generalized damped Boussinesq equation. Under small condition on the initial value, we prove the global existence and optimal decay estimate of solutions for all space dimensionsn≥1. Moreover, whenn≥2, we show that the solution can be approximated by the linear solution as time tends to infinity.

scholarly journals Asymptotic Behavior of Solutions to the Damped Nonlinear Hyperbolic Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yu-Zhu Wang
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Hyperbolic Equation ◽  
Contraction Mapping ◽  
Dimensional Space ◽  
Contraction Mapping Principle ◽  
Nonlinear Hyperbolic Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Initial Value ◽  
The Cauchy Problem

We consider the Cauchy problem for the damped nonlinear hyperbolic equation inn-dimensional space. Under small condition on the initial value, the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces are obtained by the contraction mapping principle.

scholarly journals Existence and uniform decay of solutions for a class of generalized plate-membrane-like systems

2006 ◽  
Vol 2006 ◽  
pp. 1-24
Author(s):  
Haihong Liu ◽  
Ning Su
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Damping ◽  
Asymptotic Behavior Of Solutions ◽  
Uniform Decay ◽  
Decay Of Solutions

We study the global existence, uniqueness, and asymptotic behavior of solutions for a class of generalized plate-membrane-like systems with nonlinear damping and source acting both interior and on boundary.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO CAHN–HILLIARD EQUATION WITH INERTIAL TERM

2012 ◽  
Vol 23 (09) ◽  
pp. 1250087 ◽  
Author(s):  
YIN-XIA WANG ◽  
ZHIQIANG WEI
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Dimensional Space ◽  
Solution Space ◽  
Contraction Mapping Principle ◽  
Asymptotic Behavior Of Solutions ◽  
Inertial Term ◽  
Hilliard Equation ◽  
The Cauchy Problem ◽  
Cahn Hilliard Equation

In this paper, we investigate the Cauchy problem for Cahn–Hilliard equation with inertial term in n-dimensional space. Based on the decay estimate of solutions to the corresponding linear equation, we define a solution space. Under small condition on the initial value, we prove the global existence and asymptotic behavior of the solution in the corresponding Sobolev spaces by the contraction mapping principle.

scholarly journals Global Existence and Energy Decay of Solutions to a Petrovsky Equation with General Nonlinear Dissipation and Source Term

2006 ◽  
Vol 13 (3) ◽  
pp. 397-410 ◽  
Author(s):  
Nour-Eddine Amroun ◽  
Abbes Benaissa
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Polynomial Growth ◽  
Source Term ◽  
Stable Set ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlinear Dissipation ◽  
Dissipative Term ◽  
Decay Of Solutions ◽  
Petrovsky Equation

Abstract We consider the nonlinearly damped semilinear Petrovsky equation and prove the global existence of its solutions by means of the stable set method in combined with the Faedo–Galerkin procedure. Furthermore, we study the asymptotic behavior of solutions when the nonlinear dissipative term 𝑔 does not necessarily have a polynomial growth near the origin.

scholarly journals Global existence of solution for multidimensional generalized double dispersion equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaoqiang Dai
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Dispersion Equation ◽  
Existence Of Solutions ◽  
Existence Of Solution ◽  
New Methods ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Double Dispersion

Abstract In this paper, we study the Cauchy problem of multidimensional generalized double dispersion equation. To prove the global existence of solutions, we introduce some new methods and ideas, and fill some gaps in the established results.

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.

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