Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval

This paper studies nonhomogeneous initial-boundary value problems for quasilinear one-dimensional odd-order equations posed on a bounded interval. For reasonable initial and boundary conditions we prove existence and uniqueness of global weak and regular solutions. Also we show the exponential decay of the obtained solution with zero boundary conditions and right-hand side, and small initial data. © 2010 Texas State University - San Marcos.