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Solvability and numerical algorithms for a class of variational data assimilation problems

Guri Marchuk, Victor Shutyaev (2010)

ESAIM: Control, Optimisation and Calculus of Variations

A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.

Solving a class of Hamilton-Jacobi-Bellman equations using pseudospectral methods

Mohsen Mehrali-Varjani, Mostafa Shamsi, Alaeddin Malek (2018)

Kybernetika

This paper presents a numerical approach to solve the Hamilton-Jacobi-Bellman (HJB) problem which appears in feedback solution of the optimal control problems. In this method, first, by using Chebyshev pseudospectral spatial discretization, the HJB problem is converted to a system of ordinary differential equations with terminal conditions. Second, the time-marching Runge-Kutta method is used to solve the corresponding system of differential equations. Then, an approximate solution for the HJB problem...

Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions

Catherine Cabuzel, Alain Pietrus (2007)

Applicationes Mathematicae

We prove the existence of a sequence ( x k ) satisfying 0 ∈ f ( x k ) + ∑ i = 1 M a i ∇ f ( x k + β i ( x k + 1 - x k ) ) ( x k + 1 - x k ) + F ( x k + 1 ) , where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.

Some applications of optimal control theory of distributed systems

Alfredo Bermudez (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we present some applications of the J.-L. Lions’ optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control

Some Applications of Optimal Control Theory of Distributed Systems

Alfredo Bermudez (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we present some applications of the J.-L. Lions' optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control

Some aspects of the variational nature of mean curvature flow

Giovanni Bellettini, Luca Mugnai (2008)

Journal of the European Mathematical Society

We show that the classical solution of the heat equation can be seen as the minimizer of a suitable functional defined in space-time. Using similar ideas, we introduce a functional ℱ on the class of space-time tracks of moving hypersurfaces, and we study suitable minimization problems related with ℱ . We show some connections between minimizers of ℱ and mean curvature flow.

Some Liouville theorems for PDE problems in periodic media

Luis Caffarelli (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Liouville problems in periodic media (i.e. the study of properties of global solutions to PDE) arise both in homogenization and dynamical systems. We discuss some recent results for minimal surfaces and free boundaries.

Currently displaying 81 – 100 of 232