The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the give...The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).展开更多
The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global wea...The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.展开更多
In this paper,we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations.Given an ap-propriate cost functional,we prove the existence of the op...In this paper,we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations.Given an ap-propriate cost functional,we prove the existence of the optimal growth rate and give some necessary conditions for optimal growth rate.展开更多
文摘The author considers the Klien-Gordon equations utt --△u+μu= f(u) (P >0, |f(u)| ≤ c|u|α+1 ). The necessary and sufficient condition of existence of global solutions is obtained for f(s)dsdx <d (d is the given constant).
基金Project supported by the Special Funds for Major State Basic Research Projects of China
文摘The authors consider the Cauchy problem with a kind of non-smooth initial data for quasilinear hyperbolic systems and obtain a necessary and sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution.
基金This research is supported by the National Natural Science Foundation of China.
文摘In this paper,we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations.Given an ap-propriate cost functional,we prove the existence of the optimal growth rate and give some necessary conditions for optimal growth rate.
