We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the e...We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.展开更多
In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated meth...In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.展开更多
Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of o...Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of overdetermined partial differential equations: Given a system of quasi-linear PDEs of first order for one unknown function we find a necessary and sufficient condition for the existence of solutions in terms of the second jet of the coefficients. This generalizes to certain quasi-linear systems of first order for several unknown functions.展开更多
文摘We study the Cauchy problem for a nonlinear evolution system with singularintegral differential terms.By means of some a priori estimates of the solution and theLeray-Schauder's fixed point theorem, we prove the existence and the uniqueness theoremsof the generalized global solution of the mentioned problem.
文摘In this paper, we concertrate our efforts on discuss asymptotic stability of linear inte grodifferential systems with time-varied confficients with large scale via Liapunov functional and decomposite - aggregated method. A group of sufficient conditions are given to guarantee asymptotic stability of zero solutions of systems.
基金supported by National Research Foundation of Republic of Korea(Grant Nos.2011-0008976 and 2010-0011841)
文摘Given a set of independent vector fields on a smooth manifold, we discuss how to find a function whose zero-level set is invariant under the flows of the vector fields. As an application, we study the solvability of overdetermined partial differential equations: Given a system of quasi-linear PDEs of first order for one unknown function we find a necessary and sufficient condition for the existence of solutions in terms of the second jet of the coefficients. This generalizes to certain quasi-linear systems of first order for several unknown functions.
