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Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms
  
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KeyWord:Blow-up scenario; Global existence; Large time behavior; Persistence property
Author NameAffiliation
Shengrui Lin Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Yiting Cai Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Jiaxi Luo Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Ziyu Xuan Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
Yicong Zhao Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China 
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Abstract:
      In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.