具有临界长度的非线性Korteweg-de Vries方程的渐近稳定性
Asymptotic stability of a nonlinear Korteweg-de Vries equation with a critical length
摘要：
研究了有限区间（0，2 π）上非线性Korteweg-de Vries方程的初边值问题.整个系统的左端点为Dirichlet边界条件，右端点为Dirichlet和Neumann均为齐次边界条件。已知原点附近的线性化系统的原点不是渐近稳定的。我们证明了该非线性系统的原点是（局部）渐近稳定的。
英文摘要：
We study an initial-boundary-value problem of a nonlinear Korteweg-de Vries equation posed on a finite interval (0,2pi). The whole system has Dirichlet boundary condition at the left end-point, and both of Dirichlet and Neumann homogeneous boundary conditions at the right end-point. It is known that the origin is not asymptotically stable for the linearized system around the origin. We prove that the origin is (locally) asymptotically stable for the nonlinear system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
