Conditions for the Input-Output Relation of Perfect-Mixing Processes to be First Order With Application to Building Ventilation Systems

1998 ◽  
Vol 120 (2) ◽  
pp. 170-176 ◽  
Author(s):  
C. C. Federspiel
Keyword(s):  
Differential Equations ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Input Output ◽  
Mixing Processes ◽  
First Order ◽  
Perfect Mixing ◽  
Building Ventilation ◽  
First Order Differential Equations ◽  
Ventilation Systems

Perfect-mixing models are commonly used for analyzing the performance of building ventilation systems. Recently, they have been used to estimate the strength of gas sources in buildings. However, buildings are generally partitioned in such a way that scalar first-order models are insufficient to completely describe the dynamic behavior of the gas transport in buildings. This paper addresses the question of when scalar, first-order differential equations are useful for describing the aggregate dynamical behavior of multi-variable perfect-mixing processes. Sufficient conditions for the input-output relation of a multi-variable perfect-mixing process to be a first-order differential equation are derived. The conditions are related to sensor location and system design. It is shown that the design condition is too restrictive to be widely applicable. Therefore, an alternative first-order relationship is derived by replacing the design condition with a leakage condition. The results enable the estimation of aggregate parameters of multi-zone ventilation systems from scalar, first-order differential equations, which substantially simplifies the estimation problem.

Necessary and sufficient conditions for oscillation of nonlinear first-order forced differential equations with several delays of neutral type

Analysis ◽  
2019 ◽  
Vol 39 (3) ◽  
pp. 97-105 ◽  
Author(s):  
Sandra Pinelas ◽  
Shyam S. Santra
Keyword(s):  
Differential Equations ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
First Order ◽  
Several Delays ◽  
Necessary And Sufficient ◽  
T Tau ◽  
First Order Differential Equations

AbstractIn this work, necessary and sufficient conditions are obtained such that every solution of nonlinear neutral first-order differential equations with several delays of the form\bigl{(}x(t)+r(t)x(t-\tau)\bigr{)}^{\prime}+\sum_{i=1}^{m}\phi_{i}(t)H\bigl{(}% x(t-\sigma_{i})\bigr{)}=f(t)is oscillatory or tends to zero as {t\rightarrow\infty.} This problem is considered in various ranges of the neutral coefficient r. Finally, some illustrating examples are presented to show that feasibility and effectiveness of main results.

scholarly journals Positive solutions of differential equations with unbounded Green’s kernel

2012 ◽  
Vol 6 (2) ◽  
pp. 159-173
Author(s):  
John Graef ◽  
Seshadev Padhi ◽  
Smita Pati ◽  
P.K. Kar
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Positive Solutions ◽  
Ecological Model ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Positive Periodic Solutions ◽  
First Order ◽  
First Order Differential Equations

Sufficient conditions are obtained for the existence/nonexistence of at least two positive periodic solutions of a class of first order differential equations having an unbounded Green?s function. An application to an ecological model with strong Allee effects is also given.

scholarly journals On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First-Order Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Abbas Badakaya Ja'afaru ◽  
Gafurjan Ibragimov
Keyword(s):  
Differential Equations ◽  
Differential Game ◽  
Infinite Number ◽  
Control Function ◽  
Sufficient Conditions ◽  
First Order ◽  
Control Functions ◽  
Pursuit And Evasion ◽  
And Control ◽  
First Order Differential Equations

We study pursuit and evasion differential game problems described by infinite number of first-order differential equations with function coefficients in Hilbert spacel2. Problems involving integral, geometric, and mix constraints to the control functions of the players are considered. In each case, we give sufficient conditions for completion of pursuit and for which evasion is possible. Consequently, strategy of the pursuer and control function of the evader are constructed in an explicit form for every problem considered.

Asymptotics for third-order nonlinear differential equations: Non-oscillatory and oscillatory cases

2021 ◽  
pp. 1-19
Author(s):  
Calogero Vetro ◽  
Dariusz Wardowski
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Order Differential Equation ◽  
Nonlinear Differential Equations ◽  
Oscillatory Behavior ◽  
Third Order ◽  
First Order ◽  
Third Order Differential Equation ◽  
Comparison Technique ◽  
First Order Differential Equations

We discuss a third-order differential equation, involving a general form of nonlinearity. We obtain results describing how suitable coefficient functions determine the asymptotic and (non-)oscillatory behavior of solutions. We use comparison technique with first-order differential equations together with the Kusano–Naito’s and Philos’ approaches.

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