2 papers
math.AP2025
Almost Global Solutions of Kirchhoff Equation
Jianjun Liu, Duohui Xiang
This paper is concerned with the original Kirchhoff equation $$\left\{\begin{aligned} & \pa_{tt}u-\Big(1+\int_{0}^Ï|\pa_xu|^2 dx\Big)\pa_{xx}u=0, \\&u(t,0)=u(t,Ï)=0. \end{aligned…
math.AP2024
A Birkhoff Normal Form Theorem for Partial Differential Equations on torus
Jianjun Liu, Duohui Xiang
We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is ba…