scholarly journals Discussion: “The Maximum Principle Approach to the Optimum One-Dimensional Journal Bearing” (Maday, C. J., 1970, ASME J. Lubr. Technol., 92, pp. 482–487)

1970 ◽  
Vol 92 (3) ◽  
pp. 487-489
Author(s):  
B. J. Hamrock
Keyword(s):  
Maximum Principle ◽  
Journal Bearing ◽  
One Dimensional ◽  
The Maximum Principle

The Maximum Principle Approach to the Optimum One-Dimensional Journal Bearing

1970 ◽  
Vol 92 (3) ◽  
pp. 482-487 ◽  
Author(s):  
C. J. Maday
Keyword(s):  
Maximum Principle ◽  
Film Thickness ◽  
Journal Bearing ◽  
Maximum Load ◽  
Load Direction ◽  
One Dimensional ◽  
The Maximum Principle ◽  
Minimum Film Thickness ◽  
Constant Viscosity ◽  
The One

Pontryagin’s Maximum Principle is used to determine the journal bearing which supports the maximum load for a given minimum film thickness and a specified load direction. The one-dimensional configuration which uses a constant-viscosity, incompressible lubricant is considered. Comparison shows that the optimum bearing carries a load about 13.5 percent greater than the maximum carried by the usual full-Sommerfeld bearing and about 121 percent greater than that carried by the half-Sommerfeld unit. The problem is formulated subject to the constraints of a fixed load direction and a specified minimum film thickness while the only boundary condition imposed is that the pressure must vanish at the inlet and at the outlet. The actual extent of the bearing is determined in the optimization process and it is shown that this extent is 360 deg. Further, the bearing is stepped with only two regions of different but constant film thickness.

scholarly journals The persistence of logconcavity for positive solutions of the one dimensional heat equation

1990 ◽  
Vol 48 (2) ◽  
pp. 246-263 ◽  
Author(s):  
G. Keady
Keyword(s):  
Maximum Principle ◽  
Heat Equation ◽  
Positive Solutions ◽  
Space Variable ◽  
Time Variable ◽  
One Dimensional ◽  
The Maximum Principle ◽  
Proof Techniques ◽  
The One

AbstractConsider positive solutions of the one dimensional heat equation. The space variable x lies in (–a, a): the time variable t in (0,∞). When the solution u satisfies (i) u (±a, t) = 0, and (ii) u(·, 0) is logconcave, we give a new proof based on the Maximum Principle, that, for any fixed t > 0, u(·, t) remains logconcave. The same proof techniques are used to establish several new results related to this, including results concerning joint concavity in (x, t) similar to those considered in Kennington [15].

Stress-driven diffusion in a drying liquid paint layer

1998 ◽  
Vol 9 (5) ◽  
pp. 447-461 ◽  
Author(s):  
B. W. VAN DE FLIERT ◽  
R. VAN DER HOUT
Keyword(s):  
Maximum Principle ◽  
Diffusion Process ◽  
Viscoelastic Material ◽  
Polymer Network ◽  
Paint Layer ◽  
Dimensional Model ◽  
One Dimensional ◽  
The Maximum Principle ◽  
The One ◽  
Liquid Paint

A model is presented for the diffusion-driven drying of a polymeric solution such as liquid paint. Included is a stress build-up and relaxation in the polymer network of the viscoelastic material, which influences the diffusion process. The behaviour of the (one-dimensional) model is analysed by means of the maximum principle and illustrated with numerical calculations.

scholarly journals Discrete Maximum Principle in One-Dimensional Heat Equation

2016 ◽  
Vol 2 ◽  
pp. 5
Author(s):  
Durga Jang K.C. ◽  
Ganesh Bahadur Basnet
Keyword(s):  
Maximum Principle ◽  
Heat Equation ◽  
Discrete Maximum Principle ◽  
Finite Difference Schemes ◽  
Discrete Version ◽  
One Dimensional ◽  
The Maximum Principle ◽  
Linear Partial Differential Equations ◽  
The One ◽  
College Of Engineering

<p>The maximum principle plays key role in the theory and application of a wide class of real linear partial differential equations. In this paper, we introduce ‘Maximum principle and its discrete version’ for the study of second-order parabolic equations, especially for the one-dimensional heat equation. We also give a short introduction of formation of grid as well as finite difference schemes and a short prove of the ‘Discrete Maximum principle’ by using different schemes of heat equation.</p><p><strong>Journal of Advanced College of Engineering and Management</strong>, Vol. 2, 2016, Page: 5-10</p>

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

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.

Optimal Control of a General Environmental Space

1986 ◽  
Vol 108 (4) ◽  
pp. 330-339 ◽  
Author(s):  
M. A. Townsend ◽  
D. B. Cherchas ◽  
A. Abdelmessih
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Moisture Content ◽  
Control Strategies ◽  
Switching Control ◽  
The Maximum Principle ◽  
Environmental Space ◽  
And Performance

This study considers the optimal control of dry bulb temperature and moisture content in a single zone, to be accomplished in such a way as to be implementable in any zone of a multi-zone system. Optimality is determined in terms of appropriate cost and performance functions and subject to practical limits using the maximum principle. Several candidate optimal control strategies are investigated. It is shown that a bang-bang switching control which is theoretically periodic is a least cost practical control. In addition, specific attributes of this class of problem are explored.

Sign in / Sign up

Export Citation Format

Share Document