Blow-up criteria for modified two-component generalization of hyper-elastic rod equation

2021 ◽  
pp. 1-18
Author(s):  
Emil Novruzov
Keyword(s):  
Blow Up ◽  
Elastic Rod ◽  
Two Component ◽  
Hyper Elastic ◽  
Rod Equation

scholarly journals Blow-Up Analysis for the Periodic Two-Component μ-Hunter-Saxton System

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Yunxi Guo ◽  
Tingjian Xiong
Keyword(s):  
Transport Equation ◽  
Wave Breaking ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Blow Up Analysis ◽  
Classic Method ◽  
Two Component ◽  
Localization Analysis ◽  
Spatially Periodic ◽  
Periodic Setting

The two-component μ-Hunter-Saxton system is considered in the spatially periodic setting. Firstly, a wave-breaking criterion is derived by employing the localization analysis of the transport equation theory. Secondly, several sufficient conditions of the blow-up solutions are established by using the classic method. The results obtained in this paper are new and different from those in previous works.

scholarly journals On the Blow-Up of Solutions of a Weakly Dissipative Modified Two-Component Periodic Camassa-Holm System

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yongsheng Mi ◽  
Chunlai Mu ◽  
Weian Tao
Keyword(s):  
Cauchy Problem ◽  
Blow Up ◽  
Strong Solutions ◽  
Well Posedness ◽  
Holm Equation ◽  
Two Component ◽  
The Cauchy Problem ◽  
Blow Up Rate

We study the Cauchy problem of a weakly dissipative modified two-component periodic Camassa-Holm equation. We first establish the local well-posedness result. Then we derive the precise blow-up scenario and the blow-up rate for strong solutions to the system. Finally, we present two blow-up results for strong solutions to the system.

Stability of blow-up solution for the two component Camassa–Holm equations

2020 ◽  
Vol 120 (3-4) ◽  
pp. 319-336
Author(s):  
Xintao Li ◽  
Shoujun Huang ◽  
Weiping Yan
Keyword(s):  
Shallow Water ◽  
Wave Breaking ◽  
Water Regime ◽  
Blow Up ◽  
Dynamical Behavior ◽  
Water Dynamics ◽  
Two Component ◽  
Breaking Mechanism ◽  
Self Similar ◽  
Shallow Water Dynamics

This paper studies the wave-breaking mechanism and dynamical behavior of solutions near the explicit self-similar singularity for the two component Camassa–Holm equations, which can be regarded as a model for shallow water dynamics and arising from the approximation of the Hamiltonian for Euler’s equation in the shallow water regime.

Blow-up phenomena of a weakly dissipative modified two-component Dullin–Gottwald–Holm system

2020 ◽  
Vol 106 ◽  
pp. 106378 ◽  
Author(s):  
Shou-Fu Tian ◽  
Jin-Jie Yang ◽  
Zhi-Qiang Li ◽  
Yi-Ren Chen
Keyword(s):  
Blow Up ◽  
Two Component

On Constructing the Unique Solution for the Necking in a Hyper-Elastic Rod

2006 ◽  
Vol 82 (3) ◽  
pp. 215-241 ◽  
Author(s):  
Hui-Hui Dai ◽  
Qinsheng Bi
Keyword(s):  
Unique Solution ◽  
Elastic Rod ◽  
Hyper Elastic
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