scholarly journals Blow-up Phenomena and Persistence Properties of Solutions to the Two-Component DGH Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-13
Author(s):  
Panpan Zhai ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Initial Data ◽  
Shallow Water ◽  
Finite Time ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Water System ◽  
Persistence Properties ◽  
Two Component ◽  
Shallow Water System

This paper is concerned with blow-up phenomena and persistence properties for an integrable two-component Dullin-Gottwald-Holm shallow water system. We give sufficient conditions on the initial data which guarantee blow-up phenomena of solutions in finite time for both periodic and nonperiodic cases, respectively. Furthermore, the persistence properties of solutions to the system are investigated.

scholarly journals Well-posedness and derivative blow-up for a dispersionless regularized shallow water system

Nonlinearity ◽  
2019 ◽  
Vol 32 (11) ◽  
pp. 4346-4376
Author(s):  
Jian-Guo Liu ◽  
Robert L Pego ◽  
Yue Pu
Keyword(s):  
Shallow Water ◽  
Blow Up ◽  
Water System ◽  
Well Posedness ◽  
Shallow Water System

scholarly journals Blow-Up of Solutions to a Novel Two-Component Rod System

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Shengrong Liu ◽  
Zhengguang Guo ◽  
Weiming Wang
Keyword(s):  
Shallow Water ◽  
Finite Time ◽  
Blow Up ◽  
Strong Solutions ◽  
Shallow Water Theory ◽  
Initial Value ◽  
Rod System ◽  
Two Component ◽  
Special Classes

We consider a novel two-component rod system which is closely connected to the shallow water theory. The present work is mainly concerned with the blow-up mechanism of strong solutions; we establish new conditions in view of some special classes of initial value to guarantee finite time blow-up of solutions.

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