scholarly journals NONLOCAL PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS FOR HYPERBOLIC EQUATION

2017 ◽  
Vol 23 (3) ◽  
pp. 18
Author(s):  
A. V. Dyuzheva
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Dynamical Boundary Conditions

scholarly journals ABOUT SOLVABILITY OF ONE PROBLEM WITH NONLOCAL CONDITIONS FOR HYPERBOLIC EQUATION

2021 ◽  
Vol 26 (4) ◽  
pp. 36-43
Author(s):  
V. A. Kirichek
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Nonlocal Conditions ◽  
Integral Condition ◽  
Generalized Solution ◽  
Loaded Equation ◽  
Apriori Estimates ◽  
The Given

In this article we consider a nonlocal problem with integral condition of the second kind for hyperbolic equation. The choice of a method for investigating problems with nonlocal conditions of the second kind depends on the type of nonintegral terms. In this article we consider the case when the nonintegral term is a trace of required function on the boundary of the domain. To investigate the solvability of the problem we use method of reduction for loaded equation with homogeneous boundary conditions. This method proved to be effective for defining a generalized solution, to obtain apriori estimates and to prove existence of unique generalized solution of the given problem.

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.

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