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 and energy decay of solutions to the Cauchy problem for a wave equation with a weakly nonlinear dissipation

2004 ◽  
Vol 2004 (11) ◽  
pp. 935-955 ◽  
Author(s):  
Abbès Benaissa ◽  
Soufiane Mokeddem
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Global Existence ◽  
Stable Set ◽  
Nonlinear Dissipation ◽  
Weakly Nonlinear ◽  
Dissipative Term ◽  
Decay Properties ◽  
Decay Of Solutions ◽  
The Cauchy Problem

We prove the global existence and study decay properties of the solutions to the wave equation with a weak nonlinear dissipative term by constructing a stable set inH1(ℝn).

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 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.

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.

Global existence, nonexistence, and decay of solutions for a wave equation of p-Laplacian type with weak and p-Laplacian damping, nonlinear boundary delay and source terms

2021 ◽  
pp. 1-16
Author(s):  
Nouri Boumaza ◽  
Billel Gheraibia
Keyword(s):  
Global Existence ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Source Terms ◽  
Delay Term ◽  
Laplacian Equation ◽  
Decay Of Solutions

In this paper, we consider the initial boundary value problem for the p-Laplacian equation with weak and p-Laplacian damping terms, nonlinear boundary, delay and source terms acting on the boundary. By introducing suitable energy and perturbed Lyapunov functionals, we prove global existence, finite time blow up and asymptotic behavior of solutions in cases p > 2 and p = 2. To our best knowledge, there is no results of the p-Laplacian equation with a nonlinear boundary delay term.

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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