Global existence and asymptotic behavior of solutions for the Klein–Gordon equations with quadratic nonlinearity in two space dimensions

1996 ◽  
Vol 222 (3) ◽  
pp. 341-362 ◽  
Author(s):  
Tohru Ozawa ◽  
Kimitoshi Tsutaya ◽  
Yoshio Tsutsumi
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Quadratic Nonlinearity ◽  
Asymptotic Behavior Of Solutions ◽  
Klein Gordon ◽  
Two Space Dimensions

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 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.

scholarly journals Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-27
Author(s):  
Ismahan Binshati ◽  
Harumi Hattori
Keyword(s):  
Asymptotic Behavior ◽  
Fourier Transform ◽  
Global Existence ◽  
Maxwell Equations ◽  
Decay Rates ◽  
Asymptotic Behavior Of Solutions ◽  
Two Fluids ◽  
The Fourier Transform ◽  
Rates Of Decay ◽  
Two Fluid

We study the global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler–Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical, and we also add friction between the two fluids. In addition, we discuss the rates of decay of Lp−Lq norms for a linear system. Moreover, we use the result for Lp−Lq estimates to prove the decay rates for the nonlinear systems.

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