Special Session 21: Evolution Equations and Integrable Systems

Solutions of weakly dissipated KdV equations with variable coefficients on a periodic domain

Shu-Ming Sun
Virginia Tech
The talk will discuss the solutions of the Cauchy problem for weakly dissipated KdV equation with variable coefficients posed on a periodic domain. The KdV type of equation has variable coefficients on the dissipative and dispersive terms. Under the condition that the integral of the coefficient for the dissipative term over a period keeps a correct sign, it is shown that the corresponding Cauchy problem admits a unique solution in appropriate Sobolev spaces and the solution possesses the sharp Kato smoothing property. Moreover, the nonlinear part of the solution has the strong Kato smoothing property and the sharp double Kato smoothing property. (This is a joint work with X. Yang. B.-Y. Zhang and N. Zhong)