scholarly journals Existence of global smooth solutions to the initial-boundary value problem for the quasi-linear wave equation with a degenerate dissipative term

1992 ◽  
Vol 98 (2) ◽  
pp. 299-327 ◽  
Author(s):  
Mitsuhiro Nakao
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Wave ◽  
Smooth Solutions ◽  
Linear Wave Equation ◽  
Dissipative Term ◽  
Global Smooth Solutions ◽  
Initial Boundary Value

scholarly journals A Wave Equation Associated with Mixed Nonhomogeneous Conditions: The Compactness and Connectivity of Weak Solution Set

2007 ◽  
Vol 2007 ◽  
pp. 1-17
Author(s):  
Nguyen Thanh Long ◽  
Le Thi Phuong Ngoc
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Initial Boundary Value

The purpose of this paper is to show that the set of weak solutions of the initial-boundary value problem for the linear wave equation is nonempty, connected, and compact.

Global Existence of Solutions for some Nonlinear Wave Equation

2014 ◽  
Vol 638-640 ◽  
pp. 1700-1704
Author(s):  
Yue Hu
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Boundary Value Problem ◽  
Nonlinear Wave Equation ◽  
Existence Of Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Dissipative Term ◽  
Global Existence Of Solutions ◽  
Initial Boundary Value

In this paper, we consider the existence of global solution to the initial-boundary value problem for some hyperbolic equation with P-Laplace operator and a nonlinear dissipative term using the compactness criteria and the monotone mapping’s method.

ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS TO THE FULL 1D HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

2002 ◽  
Vol 12 (06) ◽  
pp. 777-796 ◽  
Author(s):  
LING HSIAO ◽  
SHU WANG
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Value Problem ◽  
Stationary Solution ◽  
Hydrodynamic Model ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Smooth Solutions ◽  
One Dimensional ◽  
Global Smooth Solutions ◽  
Initial Boundary Value

In this paper, we study the asymptotic behavior of smooth solutions to the initial boundary value problem for the full one-dimensional hydrodynamic model for semiconductors. We prove that the solution to the problem converges to the unique stationary solution time asymptotically exponentially fast.

Energy decay for the wave equation with a degenerate dissipative term

1985 ◽  
Vol 100 (1-2) ◽  
pp. 19-27 ◽  
Author(s):  
Mitsuhiro Nakao
Keyword(s):  
Wave Equation ◽  
Boundary Value Problem ◽  
Bounded Domain ◽  
Nonnegative Function ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Decay Estimates ◽  
Dissipative Term ◽  
Image Position ◽  
Initial Boundary Value

SynopsisDecay estimates for the energy are derived for the initial boundary value problem of the wave equation with a degenerate dissipative term:where Ω is a bounded domain in Rn, a(×) is a nonnegative function such that a1 ∊Lp(Ω) for some p > 0 and f is a function tending to 0 rapidly as t → ∞

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