2 papers
math.DS2018
On the Growth in time of Sobolev Norms for Time Dependent Linear Generalized KdV-type Equations
Chengming Cao, Xaioping Yuan
We give a detailed description in 1-D the growth of Sobolev norms for time dependent linear generalized KdV-type equations on the circle. For most initial data, the growth of Sobol…
math.DS2016
Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities
Chengming Cao, Xiaoping Yuan
{\bf Abstract}: The existence of 2-dimensional KAM tori is proved for the perturbed generalized nonlinear vibrating string equation with singularities $u_{tt}=((1-x^2)u_x)_x-mu-u^3…