Necessary Conditions for Hyperbolicity of First Order Systems

Author(s):  
Antonio Bove ◽  
Tatsuo Nishitani
1969 ◽  
Vol 91 (2) ◽  
pp. 185-189 ◽  
Author(s):  
M. Wittler ◽  
C. N. Shen

A problem in the optimal control of a nuclear rocket requires the minimization of a functional subject to an integral equation constraint and an integrodifferential inequality constraint. A theorem giving first-order necessary conditions is derived for this problem in the form of a multiplier rule. The existence of multipliers and the arbitrariness of certain variations is shown. The fundamental lemma of the calculus of variations is applied. A simple example demonstrates the applicability of the theorem.


2018 ◽  
Vol 100 (3) ◽  
pp. 241-285
Author(s):  
Daniel Vázquez

Abstract This paper argues that Plato’s gigantomachia is simultaneously concerned with first-order arguments about metaphysics and epistemology and with second-order arguments that reflect on the impact of ethical components, argumentative strategies and theoretical assumptions in the conversation. This complex argumentative structure reveals, I suggest, an organic and systematic conception of philosophy where all the elements are interdependent. This interpretation has four consequences, two at the second-order level, and two concerning the first-order arguments. First, it shows that there are methodological and ethical requirements without which philosophy is impossible. Second, it shows that the text does not refute materialism but tries to reflect the necessary conditions to consider possible the existence of incorporeal beings. Third, it argues that the text assumes a conception of knowledge where knowing something is a complex activity composed of two causal relations. Finally, it offers a new interpretation of the overall conclusion of the passage.


2015 ◽  
Vol 4 (4) ◽  
pp. 311-325 ◽  
Author(s):  
Pierluigi Colli ◽  
Gianni Gilardi ◽  
Jürgen Sprekels

AbstractA boundary control problem for the pure Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first-order necessary conditions for optimality are proved.


2015 ◽  
Vol 67 (4) ◽  
pp. 942-960 ◽  
Author(s):  
Oliver Roth

AbstractIn this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin’s maximum principle from optimal control theory for the Loewner equation in several complex variables. Based on recent work of Arosio, Bracci, and Wold, we then apply our version of the Pontryagin maximum principle to obtain first-order necessary conditions for the extremal mappings for a wide class of extremal problems over the set of normalized biholomorphic mappings on the unit ball in ℂn.


Author(s):  
John E. Prussing

Optimal trajectories are analysed, covering both constant- and variable-specific-impulse cases. Primer vector is defined and illustrated. The first-order necessary conditions for an optimal constant-specific-impulse (CSI) trajectory were first derived by Lawden using classical Calculus of Variations. Variable-specific-impulse rocket engines are discussed with the cost functional for a VSI engine. In the derivation that follows, an Optimal Control Theory formulation is used, but the derivation is similar to that of Lawden. One difference is that the mass is not defined as a state variable, but is kept track of indirectly.


Author(s):  
Zhongjiao Shi ◽  
Liangyu Zhao

The coning motion is a basic angular behavior of spinning missiles. Research on the stability of coning motion is always active. In this paper, the integrated nonlinear governing equations of rigid-elastic angular motion for a spinning missile with high fineness ratio are derived firstly following the Lagrangian approach. Secondly, a set of linear equation is obtained under some assumptions considering the first order vibration mode in the form of complex summation for theoretical analysis. Finally, the sufficient and necessary conditions of coning motion dynamic stability for spinning missile with and without an acceleration autopilot are analytically derived and verified by numerical simulations based on the linear equation. It is concluded that the aeroelasticity can shrink the stable region of the design parameters, even lead to a divergent coning motion.


2018 ◽  
Vol 10 (6) ◽  
pp. 63
Author(s):  
Gossan D. Pascal Gershom ◽  
Bailly Balè ◽  
Yoro Gozo

The main goal of this paper is to establish the first order necessary optimality conditions for a tumor growth model that evolves due to cancer cell proliferation. The phenomenon is modeled by a system of three-dimensional partial differential equations. We prove the existence and uniqueness of optimal control and necessary conditions of optimality are established by using the variational formulation.


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