This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).
In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.
In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from inf...In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions of the nonlinear problem for all parameter values in that interval.展开更多
This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some unifor...This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some uniform boundedness properties.Moreover,the well-posedness and the asymptotic stability of solutions in Marcinkiewicz spaces are studied.The results are achieved by means of an appropriate estimation of the system nonlinearity in the course of an analysis based on Duhamel-type representation formulae and the Kato-Fujita framework which consists in constructing a fixed-point argument by using a suitable time-dependent space.展开更多
Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-...Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-infinity)control approach is developed for this control problem.The dynamic model of the satellite's attitude dynamics undergoesfirst approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude dynamics.For the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is designed.To compute the controller's feedback gains,an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.展开更多
文摘This paper is concerned with the generalzed global solution and its asymptotic properties for the initial value problem of the partial differential equationu t+u x 3 =F(u).
基金Supported by the NNSF of China(10441002)Supported by NNSF of Henan Province(200510466011)
文摘In this paper we study the decay estimate of global solutions to the initial-boundary value problem for double degenerate nonlinear parabolic equation by using a dif-ference inequality.
基金supported by the National Natural Science Foundation of China (11871250),Qing Lan ProjectKey (large) projects of Shandong Institute of Finance in2019 (2019SDJR31)the teaching reform project of Qilu Normal University (jg201710)
文摘In this article, by employing an oscillatory condition on the nonlinear term,a result is proved for the existence of connected component of solutions set of a nonlocal boundary value problem, which bifurcates from infinity and asymptotically oscillates over an interval of parameter values. An interesting and immediate consequence of such oscillation property of the connected component is the existence of infinitely many solutions of the nonlinear problem for all parameter values in that interval.
基金supported by the National Research and Development Agency of Chile(ANID)-Chile under Fondecyt(Grant No.1181084)。
文摘This work is concerned with the time-fractional doubly parabolic Keller-Segel system in R^(N)(N≥1),and we derive some refined results on the large time behavior of solutions which are presupposed to enjoy some uniform boundedness properties.Moreover,the well-posedness and the asymptotic stability of solutions in Marcinkiewicz spaces are studied.The results are achieved by means of an appropriate estimation of the system nonlinearity in the course of an analysis based on Duhamel-type representation formulae and the Kato-Fujita framework which consists in constructing a fixed-point argument by using a suitable time-dependent space.
基金supported by the National Natural Science Foundation of China(No.30470268 and 11461024)National Higher-education Institution General Research and Development Project(No.2014YB023)Startup Project of Doctor Scientific Research of Northwest A&F University(No.Z109021414)
文摘Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites'state-space model.In this paper,a novel nonlinear optimal(H-infinity)control approach is developed for this control problem.The dynamic model of the satellite's attitude dynamics undergoesfirst approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm.The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude dynamics.For the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is designed.To compute the controller's feedback gains,an algebraic Riccati equation is solved at each time-step of the control method.The stability properties of the control scheme are proven through Lyapunov analysis.It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.
