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Displaying 2021 – 2040 of 2165

Optimal control of nonlinear one-dimensional periodic wave equation with x-dependent coefficients

Hengyan Li, Shuguan Ji (2011)

Open Mathematics

This paper is concerned with an optimal control problem governed by the nonlinear one dimensional periodic wave equation with x-dependent coefficients. The control of the system is realized via the outer function of the state. Such a model arises from the propagation of seismic waves in a nonisotropic medium. By investigating some important properties of the linear operator associated with the state equation, we obtain the existence and regularity of the weak solution to the state equation. Furthermore,...

Optimal control of nonsmooth system governed by quasi-linear elliptic equations.

Gong, Liutang, Fei, Pusheng (1997)

International Journal of Mathematics and Mathematical Sciences

Optimal control of non-well-posed distributed systems

Jacques Louis Lions (1985)

Banach Center Publications

Optimal control of semilinear parabolic equations with state-constraints of bottleneck type

Maïtine Bergounioux, Fredi Tröltzsch (1999)

ESAIM: Control, Optimisation and Calculus of Variations

Optimal Control of Semilinear Parabolic Equations with State-Constraints of Bottleneck Type

Maïtine Bergounioux, Fredi Tröltzsch (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider optimal distributed and boundary control problems for semilinear parabolic equations, where pointwise constraints on the control and pointwise mixed control-state constraints of bottleneck type are given. Our main result states the existence of regular Lagrange multipliers for the state-constraints. Under natural assumptions, we are able to show the existence of bounded and measurable Lagrange multipliers. The method is based on results from the theory of continuous linear programming...

Optimal control of systems determined by strongly nonlinear operator valued measures

N.U. Ahmed (2008)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a class of distributed parameter systems (partial differential equations) determined by strongly nonlinear operator valued measures in the setting of the Gelfand triple V ↪ H ↪ V* with continuous and dense embeddings where H is a separable Hilbert space and V is a reflexive Banach space with dual V*. The system is given by dx + A(dt,x) = f(t,x)γ(dt) + B(t)u(dt), x(0) = ξ, t ∈ I ≡ [0,T] where A is a strongly nonlinear operator valued measure...

Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions

Karl Kunisch, Marcus Wagner (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider optimal control problems for the bidomain equations of cardiac electrophysiology together with two-variable ionic models, e.g. the Rogers–McCulloch model. After ensuring the existence of global minimizers, we provide a rigorous proof for the system of first-order necessary optimality conditions. The proof is based on a stability estimate for the primal equations and an existence theorem for weak solutions of the adjoint system.

Optimal control of the Primitive Equations of the ocean with Lagrangian observations

Maëlle Nodet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Optimal control of unstable non linear evolution systems

Pedro Humberto Rivera Rodriguez (1984)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Optimal control problem and maximum principle for fractional order cooperative systems

G. M. Bahaa (2019)

Kybernetika

In this paper, by using the classical control theory, the optimal control problem for fractional order cooperative system governed by Schrödinger operator is considered. The fractional time derivative is considered in a Riemann-Liouville and Caputo senses. The maximum principle for this system is discussed. We first study by using the Lax-Milgram Theorem, the existence and the uniqueness of the solution of the fractional differential system in a Hilbert space. Then we show that the considered optimal...

Optimal control systems by time-dependent coefficients using CAS wavelets.

Abualrub, Taher, Sadek, Ibrahim, Abukhaled, Marwan (2009)

Journal of Applied Mathematics

Optimal convergence and a posteriori error analysis of the original DG method for advection-reaction equations

Tie Zhu Zhang, Shu Hua Zhang (2015)

Applications of Mathematics

We consider the original DG method for solving the advection-reaction equations with arbitrary velocity in $d$ space dimensions. For triangulations satisfying the flow condition, we first prove that the optimal convergence rate is of order $k + 1$ in the $L_{2}$ -norm if the method uses polynomials of order $k$ . Then, a very simple derivative recovery formula is given to produce an approximation to the derivative in the flow direction which superconverges with order $k + 1$ . Further we consider a residual-based a posteriori...

Optimal convergence of a discontinuous-Galerkin-based immersed boundary method*

Adrian J. Lew, Matteo Negri (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, Int. J. Numer. Methods Eng.76 (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...

Optimal convergence of a discontinuous-Galerkin-based immersed boundary method*

Adrian J. Lew, Matteo Negri (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Optimal convergence rates of $h p$ mortar finite element methods for second-order elliptic problems

Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Optimal convergence rates of hp mortar finite element methods for second-order elliptic problems

Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present an improved, near-optimal hp error estimate for a non-conforming finite element method, called the mortar method (M0). We also present a new hp mortaring technique, called the mortar method (MP), and derive h, p and hp error estimates for it, in the presence of quasiuniform and non-quasiuniform meshes. Our theoretical results, augmented by the computational evidence we present, show that like (M0), (MP) is also a viable mortaring technique for the hp method.

Optimal convergence results for the Brezzi-Pitkäranta approximation of the Stokes problem: Exterior domains

Serguei A. Nazarov, Maria Specovius-Neugebauer (2008)

Banach Center Publications

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 $H^{5 / 2 - δ}$ convergence for the velocity part and $H^{3 / 2 - δ}$ convergence for the pressure to the solution of the Stokes problem, with δ arbitrarily...

Optimal design problems for a dynamic viscoelastic plate. I. Short memory material

Igor Bock (1995)

Applications of Mathematics

We deal with an optimal control problem with respect to a variable thickness for a dynamic viscoelastic plate with velocity constraints. The state problem has the form of a pseudohyperbolic variational inequality. The existence and uniqueness theorem for the state problem and the existence of an optimal thickness function are proved.

Optimal energy decay rate of coupled wave equations.

Benaddi, Ahmed (2004)

Portugaliae Mathematica. Nova Série

Optimal error estimates for FEM approximations of dynamic nonlinear shallow shells

Irena Lasiecka, Rich Marchand (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Finite element semidiscrete approximations on nonlinear dynamic shallow shell models in considered. It is shown that the algorithm leads to global, optimal rates of convergence. The result presented in the paper improves upon the existing literature where the rates of convergence were derived for small initial data only [19].

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