This article is concerned with a class of hyperbolic inverse source problem with memory term and nonlinear boundary damping. Under appropriate assumptions on the initial data and pa- rameters in the equation, we estab...This article is concerned with a class of hyperbolic inverse source problem with memory term and nonlinear boundary damping. Under appropriate assumptions on the initial data and pa- rameters in the equation, we establish two results on behavior of solutions. At first we proved stability of solutions when the integral overdetermination tends to zero as time goes to infinity and finally a blow-up result is established for certain solution with positive initial energy.展开更多
Morgan’s problem for a type of nonsquare systems is discussed.Necessary and sufficient conditions for the solution of the problem are obtained.And an algorithm to judge solvability of Morgan’s problem in the discuss...Morgan’s problem for a type of nonsquare systems is discussed.Necessary and sufficient conditions for the solution of the problem are obtained.And an algorithm to judge solvability of Morgan’s problem in the discussed case is provided.展开更多
One of the fundamental issues in Control Theory is to design feedback controls.It is well-known that,the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exac...One of the fundamental issues in Control Theory is to design feedback controls.It is well-known that,the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks.To date,the same problem in the stochastic setting is only partially well-understood.In this paper,we establish the equivalence between the existence of optimal feedback controls for the stochastic linear quadratic control problems with random coefficients and the solvability of the corresponding backward stochastic Riccati equations in a suitable sense.We also give a counterexample showing the nonexistence of feedback controls to a solvable stochastic linear quadratic control problem.This is a new phenomenon in the stochastic setting,significantly different from its deterministic counterpart.展开更多
文摘This article is concerned with a class of hyperbolic inverse source problem with memory term and nonlinear boundary damping. Under appropriate assumptions on the initial data and pa- rameters in the equation, we establish two results on behavior of solutions. At first we proved stability of solutions when the integral overdetermination tends to zero as time goes to infinity and finally a blow-up result is established for certain solution with positive initial energy.
基金Project supported by the National Natural Science Foundation of China.
文摘Morgan’s problem for a type of nonsquare systems is discussed.Necessary and sufficient conditions for the solution of the problem are obtained.And an algorithm to judge solvability of Morgan’s problem in the discussed case is provided.
基金supported by the NSF of China under grants 11471231,11221101,11231007,11301298 and 11401404the PCSIRT under grant IRT 16R53 and the Chang Jiang Scholars Program from Chinese Education Ministry+1 种基金the Fundamental Research Funds for the Central Universities in China under grant 2015SCU04A02the NSFC-CNRS Joint Research Project under grant 11711530142。
文摘One of the fundamental issues in Control Theory is to design feedback controls.It is well-known that,the purpose of introducing Riccati equations in the study of deterministic linear quadratic control problems is exactly to construct the desired feedbacks.To date,the same problem in the stochastic setting is only partially well-understood.In this paper,we establish the equivalence between the existence of optimal feedback controls for the stochastic linear quadratic control problems with random coefficients and the solvability of the corresponding backward stochastic Riccati equations in a suitable sense.We also give a counterexample showing the nonexistence of feedback controls to a solvable stochastic linear quadratic control problem.This is a new phenomenon in the stochastic setting,significantly different from its deterministic counterpart.
