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1

Wintner-type nonoscillation theorems for conformable linear Sturm-Liouville differential equations

Ishibashi Kazuki

Opuscula Mathematica

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2024

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Vol. 44, no. 5

727--748

EN

In this study, we addressed the nonoscillation of the Sturm-Liouville differential equation with a differential operator, which corresponds to a proportional-derivative controller. The equation is a conformable linear differential equation. A Wintner-type nonoscillation theorem was established to be applied to such equations. Using this theorem, we provided a sharp nonoscillation condition that guarantees that all nontrivial solutions to Euler-type conformable linear equations do not oscillate. The main nonoscillation theorems can be proven by introducing a Riccati inequality, which corresponds to the conformable linear equation of the Sturm-Liouville type.

2

Nonoverlapping domain decomposition for optimal control problems governed by semilinear models for gas ﬂow in networks

Leugering G., Martin A., Schmidt M., Sirvent M.

Control and Cybernetics

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2017

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Vol. 46, no. 3

191--225

EN

We consider optimal control problems for gas ﬂow in pipeline networks. The equations of motion are taken to be represented by a ﬁrst-order system of hyperbolic semilinear equations derived from the fully nonlinear isothermal Euler gas equations. We formulate an optimal control problem on a network and introduce a tailored time discretization thereof. In order to further reduce the complexity, we consider an instantaneous control strategy. The main part of the paper is concerned with a nonoverlapping domain decomposition of the optimal control problem on the graph into local problems on smaller sub-graphs—ultimately on single edges. We prove convergence of the domain decomposition method on networks and study the wellposedness of the corresponding time-discrete optimal control problems. The point of the paper is that we establish virtual control problems on the decomposed subgraphs such that the corresponding optimality systems are in fact equal to the systems obtained via the domain decomposition of the entire optimality system.

3

Oscillation on the left and on the right

Ohriska J.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

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2009

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Vol. 14

87-95

EN

In the present paper we derive sufficient conditions for the linear differential equation (r(t)y′(t))′+p(t)y(t) = 0 to be either oscillatory or non-oscillatory on the left and eventually on the right. Some estimations of count of zero point s for solutions to considered equation on an interval are also presented.

4

Stationary configurations for the average distance functional and related problems

Buttazzo G., Mainini E., Stepanov E.

Control and Cybernetics

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2009

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Vol. 38, no 4A

1107-1130

EN

For a functional defined on the class of closed one-dimensional connected subsets of Rn we consider the corresponding minimization problem and we give suitable first order necessary conditions of optimality. The cases studied here are the average distance functional arising in the mass transportation theory, and the energy related to an elliptic PDE.

5

Viscous transonic airfoil flow simulation

Dumitrescu H., Frunzulica F.

International Journal of Applied Mechanics and Engineering

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2004

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Vol. 9, no 4

687-699

EN

A calculation method for the subsonic and transonic viscous flow over airfoil using the displacement surface concept is described. This modelling technique uses a finite volume method for the time-dependent Euler equations and laminar and turbulent boundary-layer integral methods. Additionally special models for transition, laminar or turbulent separation bubbles and trailing edge treatment have been selected. However, the flow is limited to small parts of trailing edge-type separation. Comparisons with experimental data and other methods are shown.