Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 27, pp. 1-18.

Title: Persistence properties of solutions for multi-component Novikov equations

Authors: Xin Liu (Wuhan Univ. of Technology, Wuhan, China)
         Xinglong Wu (Guangdong Univ. of Foreign Studies, Guangzhou, China)
  
Abstract:
In this article, we investigate the asymptotic behavior of the solution 
for a multi-component Novikov equation in weighted Sobolev spaces. 
We introduce a set of weighted functions, and prove that the strong 
solution will retain the corresponding decay properties when the initial 
data $U_0(x)$ and its derivative $U_{0,x}(x)$ decay logarithmically, 
algebraically, and exponentially at infinity.

Submitted November 21, 2024. Published March 13, 2025.
Math Subject Classifications: 35G25, 35L05.
Key Words: Multi-component Novikov equation; asymptotic properties; 
   logarithmic decay; algebraical decay; exponential decay.