Some First-Order Nonlinear Differential Equations

2019 ◽  
pp. 21-45
Author(s):  
Ravi P. Agarwal ◽  
Simona Hodis ◽  
Donal O’Regan
Keyword(s):  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
First Order

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.

scholarly journals Integrability via Functional Expansion for the KMN Model

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1819
Author(s):  
Radu Constantinescu ◽  
Aurelia Florian
Keyword(s):  
Differential Equations ◽  
Traveling Wave ◽  
Nonlinear Differential Equations ◽  
Traveling Wave Solutions ◽  
Auxiliary Equation ◽  
First Order ◽  
Second Order Differential Equations ◽  
Functional Expansion ◽  
Wave Solutions ◽  
First Time

This paper considers issues such as integrability and how to get specific classes of solutions for nonlinear differential equations. The nonlinear Kundu–Mukherjee–Naskar (KMN) equation is chosen as a model, and its traveling wave solutions are investigated by using a direct solving method. It is a quite recent proposed approach called the functional expansion and it is based on the use of auxiliary equations. The main objectives are to provide arguments that the functional expansion offers more general solutions, and to point out how these solutions depend on the choice of the auxiliary equation. To see that, two different equations are considered, one first order and one second order differential equations. A large variety of KMN solutions are generated, part of them listed for the first time. Comments and remarks on the dependence of these solutions on the solving method and on form of the auxiliary equation, are included.

Model Based Temperature Control in RTP Yielding ±0.1 °C accuracy on A 1000 °C, 2 second, 100 °C/s Spike Anneal

1998 ◽  
Vol 525 ◽  
Author(s):  
Peter Vandenabeele ◽  
Wayne Renken
Keyword(s):  
Differential Equations ◽  
Temperature Control ◽  
Control Method ◽  
Nonlinear Differential Equations ◽  
System Response ◽  
Model Based Control ◽  
First Order ◽  
Model Based ◽  
Measured System ◽  
Spike Anneal

ABSTRACTA Model Based Control method is presented for accurate control of RTP systems. The model uses 4 states: lamp filament temperature, wafer temperature, quartz temperature and TC temperature. A set of 4 first order, nonlinear differential equations describes the model. Feedback is achieved by updating the model, based on a comparison between actual (measured) system response and modeled system response.

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