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Relevant bibliographies by topics / Neumann boundary control problems

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Journal articles

Academic literature on the topic 'Neumann boundary control problems'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Neumann boundary control problems"

1

López, Ginés, and Juan-Aurelio Montero-Sánchez. "Neumann boundary value problems across resonance." ESAIM: Control, Optimisation and Calculus of Variations 12, no. 3 (2006): 398–408. http://dx.doi.org/10.1051/cocv:2006009.

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2

Kowalewski, Adam, and Anna Krakowiak. "Optimal boundary control problems of retarded parabolic systems." Archives of Control Sciences 23, no. 3 (2013): 261–79. http://dx.doi.org/10.2478/acsc-2013-0016.

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Abstract Optimal boundary control problems of retarded parabolic systems are presented. Necessary and sufficient conditions of optimality are derived for the Neumann problem. A simple example of application is also presented.

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3

Bollo, Carolina M., Claudia M. Gariboldi, and Domingo A. Tarzia. "Neumann boundary optimal control problems governed by parabolic variational equalities." Control and Cybernetics 50, no. 2 (2021): 227–52. http://dx.doi.org/10.2478/candc-2021-0012.

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Abstract We consider a heat conduction problem S with mixed boundary conditions in an n-dimensional domain Ω with regular boundary and a family of problems Sα with also mixed boundary conditions in Ω, where α > 0 is the heat transfer coefficient on the portion of the boundary Γ1. In relation to these state systems, we formulate Neumann boundary optimal control problems on the heat flux q which is definite on the complementary portion Γ2 of the boundary of Ω. We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system state and the adjoint state when the heat transfer coefficient α goes to infinity. Furthermore, we formulate particular boundary optimal control problems on a real parameter λ, in relation to the parabolic problems S and Sα and to mixed elliptic problems P and Pα . We find an explicit form for the optimal controls, we prove monotony properties and we obtain convergence results when the parameter time goes to infinity.

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4

Hamamuki, Nao, and Qing Liu. "A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 13. http://dx.doi.org/10.1051/cocv/2019076.

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This paper is devoted to deterministic discrete game-theoretic interpretations for fully nonlinear parabolic and elliptic equations with nonlinear dynamic boundary conditions. It is known that the classical Neumann boundary condition for general parabolic or elliptic equations can be generated by including reflections on the boundary to the interior optimal control or game interpretations. We study a dynamic version of such type of boundary problems, generalizing the discrete game-theoretic approach proposed by Kohn-Serfaty (2006, 2010) for Cauchy problems and later developed by Giga-Liu (2009) and Daniel (2013) for Neumann type boundary problems.

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5

Gunzburger, Max D., Hyung-Chun Lee, and Jangwoon Lee. "Error Estimates of Stochastic Optimal Neumann Boundary Control Problems." SIAM Journal on Numerical Analysis 49, no. 4 (2011): 1532–52. http://dx.doi.org/10.1137/100801731.

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6

Eppler, Karsten, and Helmut Harbrecht. "Tracking Neumann Data for Stationary Free Boundary Problems." SIAM Journal on Control and Optimization 48, no. 5 (2010): 2901–16. http://dx.doi.org/10.1137/080733760.

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7

Werner, K. D. "Boundary value control problems involving the bessel differential operator." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 27, no. 4 (1986): 453–72. http://dx.doi.org/10.1017/s0334270000005075.

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AbstractIn this paper, we consider the hyperbolic partial differential equation wrr = wrr + 1/r wr − ν2 /r2w, where v ≥ 1/2 or ν = 0 is aprameter, with the Dirichlet, Neumann and mixed boundary conditions. The boundary controllability for such problems is investigated. The main resutl is that all “finite energy” intial states can be steered to the zero state in time T, using a control f ∈ L2 (0, T), provided T > 2. Furthermore, necessary conditions for controllability are also presented.

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8

Kowalewski, Adam, and Marek Miśkowicz. "Extremal Problems for Infinite Order Parabolic Systems with Boundary Conditions Involving Integral Time Lags." Pomiary Automatyka Robotyka 26, no. 4 (2022): 37–42. http://dx.doi.org/10.14313/par_246/37.

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Extremal problems for integral time lag infinite order parabolic systems are studied in the paper. An optimal boundary control problem for distributed infinite order parabolic systems in which integral time lags appear in the Neumann boundary conditions is solved. Such equations constitute in a linear approximation a universal mathematical model for many diffusion processes (e.g., modeling and control of heat transfer processes). The time horizon is fixed. Using the Dubovicki-Milutin framework, the necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance indexes and constrained control are derived.

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9

Wong, Kar Hung. "On the computational algorithms for time-lag optimal control problems." Bulletin of the Australian Mathematical Society 32, no. 2 (1985): 309–11. http://dx.doi.org/10.1017/s0004972700009989.

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In this thesis we study the following two types of hereditary optimal control problems: (i) problems governed by systems of ordinary differential equations with discrete time-delayed arguments appearing in both the state and the control variables; (ii) problems governed by parabolic partial differential equations with Neumann boundary conditions involving time-delays.

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10

Krumbiegel, K., and J. Pfefferer. "Superconvergence for Neumann boundary control problems governed by semilinear elliptic equations." Computational Optimization and Applications 61, no. 2 (2014): 373–408. http://dx.doi.org/10.1007/s10589-014-9718-0.

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