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Volume 4, Issue 2
Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

Shengrui Lin, Yiting Cai, Jiaxi Luo, Ziyu Xuan & Yicong Zhao

DOI: 10.12150/jnma.2022.220

J. Nonl. Mod. Anal., 4 (2022), pp. 220-244.

Published online: 2022-06

[An open-access article; the PDF is free to any online user.]

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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.

  • Keywords

Blow-up scenario, Global existence, Large time behavior, Persistence property.

  • AMS Subject Headings

34G20, 35A01

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-4-220, author = {Lin , ShengruiCai , YitingLuo , JiaxiXuan , Ziyu and Zhao , Yicong}, title = {Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2022}, volume = {4}, number = {2}, pages = {220--244}, 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2022.220}, url = {http://global-sci.org/intro/article_detail/jnma/20705.html} }
TY - JOUR T1 - Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms AU - Lin , Shengrui AU - Cai , Yiting AU - Luo , Jiaxi AU - Xuan , Ziyu AU - Zhao , Yicong JO - Journal of Nonlinear Modeling and Analysis VL - 2 SP - 220 EP - 244 PY - 2022 DA - 2022/06 SN - 4 DO - http://doi.org/10.12150/jnma.2022.220 UR - https://global-sci.org/intro/article_detail/jnma/20705.html KW - Blow-up scenario, Global existence, Large time behavior, Persistence property. AB -

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.

Shengrui Lin, Yiting Cai, Jiaxi Luo, Ziyu Xuan & Yicong Zhao. (2022). Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms. Journal of Nonlinear Modeling and Analysis. 4 (2). 220-244. doi:10.12150/jnma.2022.220
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