The maximum principle for an elliptic ? Parabolic equation of the second order

1973 ◽  
Vol 13 (4) ◽  
pp. 533-545 ◽  
Author(s):  
L. I. Kamynin ◽  
B. N. Khimchenko
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Second Order ◽  
The Maximum Principle

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

scholarly journals Maximum principle and its extension for bounded control problems with boundary conditions

2004 ◽  
Vol 2004 (35) ◽  
pp. 1855-1879 ◽  
Author(s):  
Olga Vasilieva
Keyword(s):  
Maximum Principle ◽  
Boundary Conditions ◽  
Second Order ◽  
Necessary Condition ◽  
Control Problems ◽  
Bounded Control ◽  
Singular Controls ◽  
Bounded Control Problems ◽  
The Maximum Principle ◽  
First Order

This note is focused on a bounded control problem with boundary conditions. The control domain need not be convex. First-order necessary condition for optimality is obtained in the customary form of the maximum principle, and second-order necessary condition for optimality of singular controls is derived on the basis of second-order increment formula using the method of increments along with linearization approach.

Saint-Venant’s Principle and the Torsion of Thin Shells of Revolution

1976 ◽  
Vol 43 (4) ◽  
pp. 663-667 ◽  
Author(s):  
C. O. Horgan ◽  
L. T. Wheeler
Keyword(s):  
Maximum Principle ◽  
Exponential Decay ◽  
Elliptic Equations ◽  
Second Order ◽  
Thin Shells ◽  
Shells Of Revolution ◽  
Quantitative Characterization ◽  
Elastic Shells ◽  
The Maximum Principle

This paper is concerned with obtaining stress estimates for the problem of axisymmetric torsion of thin elastic shells of revolution subject to self-equilibrated end loads. The results are obtained in the form of explicit pointwise stress bounds exhibiting an exponential decay with distance from the ends, thus supplying a quantitative characterization of Saint-Venant’s principle for this problem. In contrast to arguments using energy inequalities, here we apply a technique, recently developed by the authors, based on the maximum principle for second-order uniformly elliptic equations.

scholarly journals Unique Continuation Property of Non-Positive Weak Subsolutions for Parabolic Equations of Higher Order

1964 ◽  
Vol 24 ◽  
pp. 241-248
Author(s):  
Kazunari Hayashida
Keyword(s):  
Maximum Principle ◽  
Differential Operator ◽  
Parabolic Equations ◽  
Unique Continuation ◽  
Second Order ◽  
Wide Sense ◽  
The Maximum Principle ◽  
Unique Continuation Property ◽  
Continuation Property ◽  
Order Continuous

When L is a parabolic differential operator of second order, Nirenberg [6] proved the maximum principle for the function u which has second order continuous derivatives and satisfies Lu≧0. Recently Friedman [2] has proved the maximum principle for the measurable function satisfying Lu≧O in the wide sense. This function is named a weakly L-subparabolic function. On the other hand, Littman [5] earlier than Friedman, has defined a weakly A- subharmonic function for an elliptic differential operator A of second order and has showed the maximum principle for it.

Some Applications of the Maximum Principle to Second-Order Systems, Subject to Input Saturation, Minimizing Error, and Effort

1964 ◽  
Vol 86 (1) ◽  
pp. 11-21 ◽  
Author(s):  
G. Boyadjieff ◽  
D. Eggleston ◽  
M. Jacques ◽  
H. Sutabutra ◽  
Y. Takahashi
Keyword(s):  
Maximum Principle ◽  
Closed Loop ◽  
Input Saturation ◽  
Second Order ◽  
Performance Criteria ◽  
Closed Loop Control ◽  
Optimal Controls ◽  
Loop Control ◽  
The Maximum Principle ◽  
Second Order Systems

The optimal controls for various types of performance criteria are investigated for second-order systems by means of the Pontryagin’s Maximum Principle. Optimal control solutions for several examples are shown. The results presented show widely different modes of control depending upon the performance criteria, and also indicate a possibility of closed loop control. The methods used in the various solutions may be extended to other performance criteria and systems.

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