Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

[摘要] In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

[发布机构] University:California Institute of Technology;Department:Engineering and Applied Science

[关键词] Applied Mathematics