O 19. a 20. Hilbertově problému
On a boundary value problem in nonlinear theory of thin elastic plates
On a hyperbolic coefficient inverse problem via partial dynamic boundary measurements.
On a Lagrange problem and its generalizations
On a shape control problem for the stationary Navier-Stokes equations
On a shape control problem for the stationary Navier-Stokes equations
An optimal shape control problem for the stationary Navier-Stokes system is considered. An incompressible, viscous flow in a two-dimensional channel is studied to determine the shape of part of the boundary that minimizes the viscous drag. The adjoint method and the Lagrangian multiplier method are used to derive the optimality system for the shape gradient of the design functional.
On a Theorem of Ingham.
On an optimal control problem for a quasilinear parabolic equation
An optimal control problem governed by a quasilinear parabolic equation with additional constraints is investigated. The optimal control problem is converted to an optimization problem which is solved using a penalty function technique. The existence and uniqueness theorems are investigated. The derivation of formulae for the gradient of the modified function is explainedby solving the adjoint problem.
On Bellman equations of ergodic control in ...n.
On closure of the pre-images of families of mappings
The closures of the pre-images associated with families of mappings in different topologies of normed spaces are considered. The question of finding a description of these closures by means of families of the same kind as original ones is studied. It is shown that for the case of the weak topology this question may be reduced to finding an appropriate closure of a given family. There are discussed various situations when the description may be obtained for the case of the strong topology. An example...
On control problems of minimum time for Lagrangian systems similar to a swing. I. Convexity criteria for sets
One establishes some convexity criteria for sets in . They will be applied in a further Note to treat the existence of solutions to minimum time problems for certain Lagrangian systems referred to two coordinates, one of which is used as a control. These problems regard the swing or the ski.
On control problems of minimum time for Lagrangian systems similar to a swing. II Application of convexity criteria to certain minimum time problems
This Note is the Part II of a previous Note with the same title. One refers to holonomic systems with two degrees of freedom, where the part can schemetize a swing or a pair of skis and schemetizes whom uses . The behaviour of is characterized by a coordinate used as a control. Frictions and air resistance are neglected. One considers on minimum time problems and one is interested in the existence of solutions. To this aim one determines a certain structural condition which implies...
On diffused-interface models of shape memory alloys
On extensions of families of operators
The strong closure of feasible states of families of operators is studied. The results are obtained for self-adjoint operators in reflexive Banach spaces and for more concrete case - families of elliptic systems encountered in the optimal layout of materials. The results show when it is possible to parametrize the strong closure by the same type of operators. The results for systems of elliptic operators for the case when number of unknown functions is less than the dimension of the reference...
On identification of critical curves
The paper deals with the problem of finding a curve, going through the interior of the domain , accross which the flux , where is the solution of a mixed elliptic boundary value problem solved in , attains its maximum.
On infinite dimensional control systems with state and control constraints
On irrotational flows through cascades of profiles in a layer of variable thickness
The paper is devoted to the study of solvability of boundary value problems for the stream function, describing non-viscous, irrotional, subsonic flowes through cascades of profiles in a layer of variable thickness. From the definition of a classical solution the variational formulation is derive and the concept of a weak solution is introduced. The proof of the existence and uniqueness of the weak solution is based on the monotone operator theory.
On minima of variational problems with some nonconvex constraints.
On nonlinear, nonconvex evolution inclusions
We consider a nonlinear evolution inclusion driven by an m-accretive operator which generates an equicontinuous nonlinear semigroup of contractions. We establish the existence of extremal integral solutions and we show that they form a dense, -subset of the solution set of the original Cauchy problem. As an application, we obtain “bang-bang”’ type theorems for two nonlinear parabolic distributed parameter control systems.
On optimal matching measures for matching problems related to the Euclidean distance
We deal with an optimal matching problem, that is, we want to transport two measures to a given place (the target set) where they will match, minimizing the total transport cost that in our case is given by the sum of two different multiples of the Euclidean distance that each measure is transported. We show that such a problem has a solution with an optimal matching measure supported in the target set. This result can be proved by an approximation procedure using a -Laplacian system. We prove...