具有Kinetic的Muskat问题古典解

考虑了具有Kinetic的多维Muskat问题，并得到了这个问题局部古典解存在唯一性。     

Minimal trajectories of nonconvex differential inclusions

We consider an optimization problem with endpoint constraints associated with a nonconvex differential inclusion. We give a necessary condition of the maximum principle type for a solution of the problem. Following the approach from Ref. 1, the condition is stated in terms of single-valued selections of the convexified right-hand side of the inclusion.This work was supported in part by the National Science Foundation, Grant No. DMS-86-01774.     

On the sufficiency of the linear maximum principle for discrete-time control problems

This note presents a family of linear maximum principles for the discrete-time optimal control problem, derived from the saddle-point theorem of mathematical programming. Some simple examples illustrate the applicability of the main theoretical results.     

Existence of solution for boundary value problem of nonlinear fractional differential equation

This paper is concerned with the boundary value problem of a nonlinear fractional differential equation.By means of Schauder fixed-point theorem,an existence result of solution is obtained.     

Lipschitzianity of optimal trajectories for the Bolza optimal control problem

In this paper we investigate Lipschitz continuity of optimal solutions for the Bolza optimal control problem under Tonelli’s type growth condition. Such regularity being a consequence of normal necessary conditions for optimality, we propose new sufficient conditions for normality of state-constrained nonsmooth maximum principles for absolutely continuous optimal trajectories. Furthermore we show that for unconstrained problems any minimizing sequence of controls can be slightly modified to get a new minimizing sequence with nice boundedness properties. Finally, we provide a sufficient condition for Lipschitzianity of optimal trajectories for Bolza optimal control problems with end point constraints and extend a result from (J. Math. Anal. Appl. 143, 301–316, 1989) on Lipschitzianity of minimizers for a classical problem of the calculus of variations with discontinuous Lagrangian to the nonautonomous case.     

An optimal control problem in the study of liver kinetics

The enzyme activities in the liver are described by a system of ordinary differential equations. A certain substance in the blood is transformed twice by different kinds of enzymes. The mathematical problem is to determine the distribution of the enzymes along the blood flow so that the outflow concentration of the once-transformed form of the substance is as small as possible. This problem has been considered before and solved for particular types of enzyme kinetics. In this paper, we solve the problem for more general types of kinetics (including substrate- inhibition kinetics). The methods used are also different, in that the problem is considered as a problem of optimal control and Pontryagin's maximum principle is applied to derive necessary conditions.     

Solvability of the boundary-value problem for a variable-order differential equation on a geometric graph

The solvability of the boundary-value problem for a string-beam model is studied. The model is described by an equation of orders 2 or 4 on dirrerent edges of an arbitrary graph. Criteria for the problem to be degenerate and nondegenerate are obtained; in particular, it is proved that the nondegeneracy of the problem is equivalent to the maximum principle.     

Necessary extremum conditions in the optimal control problem with state constraints

The optimal control problem with state constraints is examined. An alternative to the available approaches to the study of this problem is proposed. The maximum principle and second-order necessary conditions are proved.     

Dirichlet Boundary Control of Hyperbolic Equations in the Presence of State Constraints

We study optimal control problems for hyperbolic equations (focusing on the multidimensional wave equation) with control functions in the Dirichlet boundary conditions under hard/pointwise control and state constraints. Imposing appropriate convexity assumptions on the cost integral functional, we establish the existence of optimal control and derive new necessary optimality conditions in the integral form of the Pontryagin Maximum Principle for hyperbolic state-constrained systems.     

Existence of positive solution for singular fractional differential equation

In this paper, we establish the existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation. Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.     

具有逐项分数阶导数的微分方程边值问题解的存在性

研究了一类具有逐项分数阶导数的微分方程边值问题.对参数的各种取值情况进行了全面的分析,运用Banach压缩映射原理和Schauder不动点定理,得到并证明了边值问题解的存在性定理.最后,给出了两个例子来证明结论有效.     

线性-非二次最优控制问题的Near-Optimal控制

对所谓的线性-非二次最优控制问题给出了一种求其near-optimal控制的方法.     

Normality of the maximum principle for nonconvex constrained Bolza problems

We consider a Bolza optimal control problem with state constraints. It is well known that under some technical assumptions every strong local minimizer of this problem satisfies first order necessary optimality conditions in the form of a constrained maximum principle. In general, the maximum principle may be abnormal or even degenerate and so does not provide a sufficient information about optimal controls. In the recent literature some sufficient conditions were proposed to guarantee that at least one maximum principle is nondegenerate, cf. [A.V. Arutyanov, S.M. Aseev, Investigation of the degeneracy phenomenon of the maximum principle for optimal control problems with state constraints, SIAM J. Control Optim. 35 (1997) 930–952; F. Rampazzo, R.B. Vinter, A theorem on existence of neighbouring trajectories satisfying a state constraint, with applications to optimal control, IMA 16 (4) (1999) 335–351; F. Rampazzo, R.B. Vinter, Degenerate optimal control problems with state constraints, SIAM J. Control Optim. 39 (4) (2000) 989–1007]. Our aim is to show that actually conditions of a similar nature guarantee normality of every nondegenerate maximum principle. In particular we allow the initial condition to be fixed and the state constraints to be nonsmooth. To prove normality we use J. Yorke type linearization of control systems and show the existence of a solution to a linearized control system satisfying new state constraints defined, in turn, by linearization of the original set of constraints along an extremal trajectory.     

Positive solutions to m-point boundary value problem of fractional differential equation

In this paper, we study the multiplicity of positive solutions to the following m-point boundary value problem of nonlinear fractional differential equations: Dqu(t) + f(t, u(t)) = 0, 0 < t < 1, u(0) = 0, u(1) =sum (μiDpu(t)|t = ξi ) from i =1 to ∞ m-2, where q ∈R , 1 相似文献   

On the Stochastic Maximum Principle in Optimal Control of Degenerate Diffusions with Lipschitz Coefficients

We establish a stochastic maximum principle in optimal control of a general class of degenerate diffusion processes with global Lipschitz coefficients, generalizing the existing results on stochastic control of diffusion processes. We use distributional derivatives of the coefficients and the Bouleau Hirsh flow property, in order to define the adjoint process on an extension of the initial probability space. This work is partially supported by MENA Swedish Algerian Research Partnership Program (348-2002-6874) and by French Algerian Cooperation, Accord Programme Tassili, 07 MDU 0705.     

An optimal control problem for systems described by partial differential equations of hyperbolic type with delay

An optimal control problem of the Gourse type with delay is investigated. With a given aim functional, a necessary condition of optimality is formulated and proved in the form of a maximum principle. The proof is based on the reduction of a problem with delay to a problem without delay.The authors thank Prof. G. Leitmann, University of California, Berkeley, for discussions and for his interest in this paper.