Semigroup approach to the cauchy problem for the equations ut - α(u)xx + β(u)x ⇚ f with nonlinear boundary conditions

1990 ◽  
Vol 15 (9) ◽  
pp. 833-848
Author(s):  
Xiangsheng Xu
Keyword(s):  
Cauchy Problem ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
The Cauchy Problem ◽  
Semigroup Approach

Ordinary Differential Equations with Nonlinear Boundary Conditions

2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Lower And Upper Solutions ◽  
Iterative Technique ◽  
Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

Chaotic Vibration of a Two-dimensional Non-strictly Hyperbolic Equation

2018 ◽  
Vol 61 (4) ◽  
pp. 768-786 ◽  
Author(s):  
Liangliang Li ◽  
Jing Tian ◽  
Goong Chen
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Method Of Characteristics ◽  
Nonlinear Boundary ◽  
Chaotic Oscillation ◽  
Nonlinear Boundary Conditions ◽  
Rigorous Proof ◽  
Two Dimensional ◽  
Chaotic Vibration

AbstractThe study of chaotic vibration for multidimensional PDEs due to nonlinear boundary conditions is challenging. In this paper, we mainly investigate the chaotic oscillation of a two-dimensional non-strictly hyperbolic equation due to an energy-injecting boundary condition and a distributed self-regulating boundary condition. By using the method of characteristics, we give a rigorous proof of the onset of the chaotic vibration phenomenon of the zD non-strictly hyperbolic equation. We have also found a regime of the parameters when the chaotic vibration phenomenon occurs. Numerical simulations are also provided.

Boundary oscillations and nonlinear boundary conditions

2006 ◽  
Vol 343 (2) ◽  
pp. 99-104 ◽  
Author(s):  
José M. Arrieta ◽  
Simone M. Bruschi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions

Development of a New Simulation Technique Based on the Modal Approximation for Fluid Transients in Complex Pipeline Systems With Time-Variant Nonlinear Boundary Conditions

2006 ◽  
Vol 129 (6) ◽  
pp. 791-798 ◽  
Author(s):  
E. Kojima ◽  
T. Yamazaki ◽  
M. Shinada
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Safety Valve ◽  
Nonlinear Boundary Conditions ◽  
Simulation Technique ◽  
Nonlinear Relationship ◽  
Calculation Methods ◽  
Pipeline Systems ◽  
Fluid Transients ◽  
Modal Approximation

A new simulation technique called the system modal approximation method (SMA) for fluid transients in complex pipeline systems has been proposed. The superiority of this technique compared to other existing methods has been verified. Thus far, however, detailed considerations have been limited to pipelines having elementary boundary conditions. In the present paper, for the generalization of the SMA method, calculation methods are newly proposed for the case in which the boundary conditions are given by the time-variant nonlinear relationship between pressure and flow rate, such as the conditions in a safety valve, and its usefulness is verified by comparison to experimental measurements.

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