scholarly journals On solutions of the wave equation with a sublinear dissipative term

1987 ◽  
Vol 69 (2) ◽  
pp. 204-215 ◽  
Author(s):  
Mitsuhiro Nakao
Keyword(s):  
Wave Equation ◽  
Dissipative Term

scholarly journals The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Ying Wang ◽  
YunXi Guo
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Sufficient Conditions ◽  
Global Weak Solution ◽  
Dissipative Term ◽  
Shallow Water Wave ◽  
Global Strong Solution ◽  
Special Cases ◽  
The Cauchy Problem

A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that(1-∂x2)u0∈M+(R),u0∈H1(R),andu0∈L1(R), the existence and uniqueness of the global weak solution to the equation are shown to be true.

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 Non decay of the total energy for the wave equation with the dissipative term of spatial anisotropy

2004 ◽  
Vol 174 ◽  
pp. 115-126 ◽  
Author(s):  
Mishio Kawashita ◽  
Hideo Nakazawa ◽  
Hideo Soga
Keyword(s):  
Wave Equation ◽  
Total Energy ◽  
Natural Generalization ◽  
The Other ◽  
Asymptotic Solutions ◽  
Half Line ◽  
Decay Estimates ◽  
Uniform Decay ◽  
Spatial Anisotropy ◽  
Dissipative Term

AbstractWe consider the behavior of the total energy for the wave equation with the dissipative term. When the dissipative term works well uniformly in every direction, several authors obtain uniform decay estimates of the total energy. On the other hand, if the dissipative term is small enough uniformly in every direction, it is known that there exists a solution whose total energy does not decay. We examine the case that the dissipative term vanishes only in a neighborhood of a half-line. We introduce a uniform decay property, which is a natural generalization of the uniform decay estimates, and show that this property does not hold in our case. We prove this by constructing asymptotic solutions supported in the place where the dissipative term vanishes.

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.

scholarly journals Global existence of solutions to degenerate wave equations with dissipative terms

1999 ◽  
Vol 60 (1) ◽  
pp. 1-10
Author(s):  
Mohammed Aassila
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Wave Equations ◽  
Existence Of Solutions ◽  
Dissipative Term ◽  
Global Existence Of Solutions ◽  
Asymptotic Behaviour Of Solutions ◽  
Dissipative Terms ◽  
Degenerate Wave Equation

In this paper we prove the global existence and study the asymptotic behaviour of solutions to a degenerate wave equation with a nonlinear dissipative term.

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