The Cauchy problem for semilinear hyperbolic equation with characteristic degeneration on the initial hyperplane

2018 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equation ◽  
The Cauchy Problem ◽  
Semilinear Hyperbolic Equation

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 Cauchy problem for a substantially loaded hyperbolic equation

2021 ◽  
pp. 10-15
Author(s):  
А.Х. Аттаев
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equation ◽  
Vibration Equation ◽  
One Dimensional ◽  
The Cauchy Problem

В работе проводится исследование задачи Коши для существенно нагруженного уравнения колебания одномерной струны. Приводятся примеры характеристических многообразий, для которых задача Коши поставлена корректно, а также нехарактеристических многообразий, для которых задача Коши поставлено некорректно. In this work, we study the Cauchy problem for a substantially loaded vibration equation of a one-dimensional string. Examples are given of characteristic manifolds for which the Cauchy problem is posed correctly, as well as non-characteristic manifolds for which the Cauchy problem is posed incorrectly.

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