共查询到10条相似文献,搜索用时 140 毫秒
1.
S. S. Sritharan 《Applied Mathematics and Optimization》2000,41(2):255-308
This paper deals with the optimal control of space—time statistical behavior of turbulent fields. We provide a unified treatment
of optimal control problems for the deterministic and stochastic Navier—Stokes equation with linear and nonlinear constitutive
relations. Tonelli type ordinary controls as well as Young type chattering controls are analyzed. For the deterministic case
with monotone viscosity we use the Minty—Browder technique to prove the existence of optimal controls. For the stochastic
case with monotone viscosity, we combine the Minty—Browder technique with the martingale problem formulation of Stroock and
Varadhan to establish existence of optimal controls. The deterministic models given in this paper also cover some simple eddy
viscosity type turbulence closure models.
Accepted 7 June 1999 相似文献
2.
Youjun Xu Xinguang Zhang Dongyuan Liu 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5885-5894
In this paper, we consider the existence of insensitizing control for a semilinear heat equation involving gradient terms in unbounded domain Ω. In this case, we prove the existence of controls insensitizing the L2-norm of the observation of the solution in an open subset of the domain. The proofs of the main results in this paper involve such inequalities and rely on the study of these linear problems and appropriate fixed point arguments. 相似文献
3.
We study at first the solutions of a Schrödinger type problem relative to the subelliptic p-Laplacian: we prove, for potentials that are in the Kato space, an Harnack inequality on enough small intrinsic balls; the continuity of the solutions to the homogeneous Dirichlet problem follows from some estimates in the proof of the Harnack inequality. In the second part of the paper we study a relaxed Dirichlet problem for the subelliptic p-Laplacian and we prove a Wiener type criterion for the regularity of a point (with respect to our problem). 相似文献
4.
Nikolaos S. PAPAGEORGIOU Nikolaos YANNAKAKIS 《数学学报(英文版)》2005,21(5):977-996
This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x(t) and x(t). In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 (T, H). Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 (T, H) to the solutions of the original convex problem (strong relaxation). An example of a nonlinear hyperbolic optimal control problem is also discussed. 相似文献
5.
D. Ruiz 《Journal of Differential Equations》2004,199(1):96-114
In this paper we study the existence of positive solutions for a nonlinear Dirichlet problem involving the m-Laplacian. The nonlinearity considered depends on the first derivatives; in such case, variational methods cannot be applied. So, we make use of topological methods to prove the existence of solutions. We combine a blow-up argument and a Liouville-type theorem to obtain a priori estimates. Some Harnack-type inequalities which are needed in our reasonings are also proved. 相似文献
6.
V. F. Lubyshev 《Proceedings of the Steklov Institute of Mathematics》2010,269(1):160-173
We study the existence of multiple positive solutions to a nonlinear Dirichlet problem for the p-Laplacian (in a bounded domain in ℝ
N
) with a concave nonlinearity and with a nonlinear perturbation involving a function of the spatial variable whose sign can
change the character of concavity. Under two different sets of conditions imposed on the perturbation, we prove the existence
of two and three positive solutions, respectively. 相似文献
7.
Radouen Ghanem 《Positivity》2009,13(2):321-338
We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function
which is the control function is assumed in H2. We use an approximate technique to introduce a family of problems governed by variational equations. We prove optimal solutions
existence and give necessary optimality conditions.
The author is grateful to Prof. M. Bergounioux for her instructive suggestions. 相似文献
8.
E. Marušic-Paloka 《Applied Mathematics and Optimization》2000,41(3):365-375
We prove the existence of the very weak solution of the Dirichlet problem for the Navier—Stokes system with L
2
boundary data. Under the small data assumption we also prove the uniqueness. We use the penalization method to study the linearized problem and then apply Banach's fixed
point theorem for the nonlinear problem with small boundary data. We extend our result to the case with no small data assumption by splitting the data on a large regular and small irregular part.
Accepted 15 March 1999 相似文献
9.
The problem of computing Pareto optimal solutions with distributed algorithms is considered inn-player games. We shall first formulate a new geometric problem for finding Pareto solutions. It involves solving joint tangents
for the players' objective functions. This problem can then be solved with distributed iterative methods, and two such methods
are presented. The principal results are related to the analysis of the geometric problem. We give conditions under which
its solutions are Pareto optimal, characterize the solutions, and prove an existence theorem. There are two important reasons
for the interest in distributed algorithms. First, they can carry computational advantages over centralized schemes. Second,
they can be used in situations where the players do not know each others' objective functions. 相似文献
10.
We consider approximation of L
p
functions by Hardy functions on subsets of the circle for . After some preliminaries on the possibility of such an approximation which are connected to recovery problems of the Carleman
type, we prove existence and uniqueness of the solution to a generalized extremal problem involving norm constraints on the
complementary subset.
December 6, 1995. Date revised: August 26, 1996. 相似文献