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 - <p style="text-align: justify;">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.</p>