Sobolev equations for nonlinear dispersive systems^†

^†This work was supported in part by a National Science Foundation grant

Abstract

Global existence and stability results are obtained for a semifinear evolution equation of Sobolev type in a Banach space. The nonlinear term is assumed to be uniformly Lipschitz on each bounded set and to satisfy a dissipation-type inequality. Applications include various initial-boundary value problems for certain partial differential equations which have been used to model unidirectional long waves in nonlinear dispersive systems

^†This work was supported in part by a National Science Foundation grant

^†This work was supported in part by a National Science Foundation grant

Notes

^†This work was supported in part by a National Science Foundation grant