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Para el estudio de la naturaleza de formas críticas en optimización de formas se requieren algunas propiedades de continuidad sobre las derivadas de segundo orden de las formas. Dado que la fórmula de Taylor-Young involucra a diferentes topologías que no son equivalentes, dicha fórmula no permite deducir cuando una forma crítica es un mínimo local estricto de la función forma pese a que su Hessiano sea definido positivo en ese punto. El resultado principal de este trabajo ofrece una cota superior...
In this paper, we consider the solution of optimal control problem for hyperdiffusion equation involving boundary function of continuous time variable in its cost function. A specific direct approach based on infinite series of Fourier expansion in space and temporal integration by parts for analytical solution is proposed to solve optimal boundary control for hyperdiffusion equation. The time domain is divided into number of finite subdomains and optimal function is estimated at each subdomain...
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
We propose a general approach for the numerical approximation of
optimal control problems governed by a linear advection–diffusion
equation, based on a stabilization method applied to the
Lagrangian functional, rather than stabilizing the state and
adjoint equations separately. This approach yields a coherently
stabilized control problem. Besides, it allows a straightforward
a posteriori error estimate in which estimates of higher order terms
are needless. Our a posteriori estimates stems from...
We consider a distributed system in which the state q is
governed by a parabolic equation and a pair of controls v = (h,k)
where h and k play two different roles: the control k is
of controllability type while h expresses that the state q
does not move too far from a given state.
Therefore, it is natural to introduce the control
point of view. In fact, there are several ways to state and solve optimal control problems with a pair of controls h and k, in particular the Least Squares method...
We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot
expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having
defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost
functions using a non standard compactness argument. Then, we derive a first order optimality system assuming...
We study the numerical aspect of the optimal control of problems governed by a linear elliptic partial differential equation (PDE). We consider here the gas flow in porous media. The observed variable is the flow field we want to maximize in a given part of the domain or its boundary. The control variable is the pressure at one part of the boundary or the discharges of some wells located in the interior of the domain. The objective functional is a balance between the norm of the flux in the observation...
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