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Displaying 421 –
440 of
443
We study an optimal boundary control problem for the two dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle. The control acts through the Dirichlet boundary condition. We first establish the existence and uniqueness of the solution for the two-dimensional unsteady linearized compressible Navier–Stokes equations in a rectangle with inhomogeneous Dirichlet boundary data, not necessarily smooth. Then, we prove the existence and uniqueness of the optimal solution over...
An optimal control problem for a model for stationary, low Mach
number, highly nonisothermal, viscous flows is considered.
The control problem involves the minimization of a measure of
the distance between the velocity field and a given target
velocity field. The existence of solutions of a boundary value
problem for the model equations is established as is the
existence of solutions of the optimal control problem. Then, a
derivation of an optimality system, i.e., a boundary value
problem from...
We consider an optimal control problem for the three-dimensional non-linear Primitive Equations of the ocean in a vertically bounded and horizontally periodic domain. We aim to reconstruct the initial state of the ocean from Lagrangian observations. This inverse problem is formulated as an optimal control problem which consists in minimizing a cost function representing the least square error between Lagrangian observations and their model counterpart, plus a regularization term. This paper proves...
The one-dimensional steady-state convection-diffusion problem for the unknown temperature of a medium entering the interval with the temperature and flowing with a positive velocity is studied. The medium is being heated with an intensity corresponding to for a constant . We are looking for a velocity with a given average such that the outflow temperature is maximal and discuss the influence of the boundary condition at the point on the “maximizing” function .
This paper deals with a strongly elliptic perturbation for the Stokes equation in exterior three-dimensional domains Ω with smooth boundary. The continuity equation is substituted by the equation -ε²Δp + div u = 0, and a Neumann boundary condition for the pressure is added. Using parameter dependent Sobolev norms, for bounded domains and for sufficiently smooth data we prove convergence for the velocity part and convergence for the pressure to the solution of the Stokes problem, with δ arbitrarily...
An axisymmetric system of mould, glass piece, plunger and plunger cavity is considered. The state problem is given as a stationary head conduction process. The system includes the glass piece representing the heat source and is cooled inside the plunger cavity by flowing water and outside by the environment of the mould. The design variable is taken to be the shape of the inner surface of the plunger cavity. The cost functional is the second power of the norm in the weighted space of difference...
We consider a finite element discretization by
the Taylor–Hood element for the stationary
Stokes and Navier–Stokes
equations with slip boundary condition. The slip boundary condition
is enforced pointwise for nodal values of the velocity in
boundary nodes. We prove optimal error estimates in the
H1 and L2 norms for the velocity and pressure respectively.
In this paper we construct a model to describe some
aspects of the
deformation of the central region of the human lung
considered as a
continuous
elastically deformable medium. To achieve this purpose, we study
the interaction
between the pipes composing the tree and the fluid that goes
through it. We use a stationary model to determine the deformed radius of each branch. Then, we solve a constrained minimization problem, so as to minimize the viscous (dissipated) energy in the tree. The key...
We give a new proof of the Lipschitz continuity with respect to t of the pressure in a one dimensional porous medium flow. As is shown by the Barenblatt solution, this is the optimal t-regularity for the pressure. Our proof is based on the existence and properties of a certain selfsimilar solution.
We study a 2D model of the orientation distribution of fibres in a paper machine headbox. The goal is to control the orientation of fibres at the outlet by shape variations. The mathematical formulation leads to an optimization problem with control in coefficients of a linear convection-diffusion equation as the state problem. Existence of solutions both to the state and the optimization problem is analyzed and sensitivity analysis is performed. Further, discretization is done and a numerical example...
We consider the analysis and
numerical solution of a forward-backward boundary value problem.
We provide some motivation, prove existence and uniqueness in a function
class especially geared to the problem at hand, provide various energy
estimates, prove a priori error estimates for the Galerkin method,
and show the results of some numerical computations.
Currently displaying 421 –
440 of
443