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1. A gradient estimate for solutions of the heat equation. II

Creator:
Kahane, Charles S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
gradient estimate, heat equation, and maximum principle
Language:
English
Description:
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Le minimum de deux fonctions plurisousharmoniques et une nouvelle caracterisation des fonctions holomorphes

Creator:
Abidi, Jamel and Ben Yattou, Mohamed Lassaad
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
maximum principle and plurisubharmonic function
Language:
English
Description:
We prove, among other results, that min(u, v) is plurisubharmonic (psh) when u, v belong to a family of functions in psh(D) ∩ Λα(D), where Λα(D) is the α-Lipchitz functional space with 1 < α < 2. Then we establish a new characterization of holomorphic functions defined on open sets of ℂ n .
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Optimal control problem and maximum principle for fractional order cooperative systems

Creator:
Bahaa, G. M.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
optimality conditions, fractional optimal control, cooperative systems, Schrödinger operator, maximum principle, existence of solution, boundary control, fractional Caputo derivatives, and Riemann-Liouville derivatives
Language:
English
Description:
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 control problem has a unique solution. The performance index of a (FOCP) is considered as a function of both state and control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). Finally, we impose some constraints on the boundary control. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of right fractional Caputo derivative, we obtain an optimality system for the optimal control. Some examples are analyzed in details.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public