scholarly journals Asymptotic behavior of the solution to the Cauchy problem for the Timoshenko system in thermoelasticity of type III

2013 ◽  
Vol 2 (2) ◽  
pp. 423-440 ◽  
Author(s):  
Belkacem Said-Houari ◽  
◽  
Radouane Rahali ◽  
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Timoshenko System ◽  
Type Iii ◽  
The Cauchy Problem

scholarly journals Comparison between the Cauchy problem and the scattering problem for the Landau damping in the Vlasov-HMF equation

2021 ◽  
pp. 1-24
Author(s):  
Dario Benedetto ◽  
Emanuele Caglioti ◽  
Stefano Rossi
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Scattering Problem ◽  
New Method ◽  
Landau Damping ◽  
The Cauchy Problem ◽  
The One ◽  
Perturbative Result

We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this “scattering problem”, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.

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 Asymptotics for the Ostrovsky-Hunter Equation in the Critical Case

2017 ◽  
Vol 2017 ◽  
pp. 1-21
Author(s):  
Fernando Bernal-Vílchis ◽  
Nakao Hayashi ◽  
Pavel I. Naumkin
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Pseudodifferential Operator ◽  
Critical Case ◽  
Large Time ◽  
Asymptotic Behavior Of Solutions ◽  
The Cauchy Problem ◽  
Time Existence ◽  
Time Asymptotic Behavior

We consider the Cauchy problem for the Ostrovsky-Hunter equation ∂x∂tu-b/3∂x3u-∂xKu3=au, t,x∈R2,  u0,x=u0x, x∈R, where ab>0. Define ξ0=27a/b1/4. Suppose that K is a pseudodifferential operator with a symbol K^ξ such that K^±ξ0=0, Im K^ξ=0, and K^ξ≤C. For example, we can take K^ξ=ξ2-ξ02/ξ2+1. We prove the global in time existence and the large time asymptotic behavior of solutions.

The Cauchy problem of the Bresse system in thermoelasticity of type III

2015 ◽  
Vol 95 (11) ◽  
pp. 2323-2338 ◽  
Author(s):  
Belkacem Said-Houari ◽  
Taklit Hamadouche
Keyword(s):  
Cauchy Problem ◽  
Type Iii ◽  
Bresse System ◽  
The Cauchy Problem
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