A PROBLEM OF RECOVERING A SPECIAL TWO-DIMENSIONAL POTENTIAL IN A HYPERBOLIC EQUATION

2016 ◽  
Vol 4 (1) ◽  
pp. 32-46
Author(s):  
V.G. Romanov
Keyword(s):  
Hyperbolic Equation ◽  
Two Dimensional

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.

scholarly journals Recovery of unknown coefficients in a two-dimensional hyperbolic equation with additional conditions

2021 ◽  
Author(s):  
Elvin Azizbayov ◽  
He Yang ◽  
Yashar Mehraliyev
Keyword(s):  
Inverse Problem ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Original Problem ◽  
Boundary Value ◽  
Auxiliary Problem ◽  
Fourier Method ◽  
Two Dimensional ◽  
Inverse Boundary ◽  
Inverse Boundary Value Problem

In this paper, a nonlocal inverse boundary value problem for a two-dimensional hyperbolic equation with overdetermination conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary value problem and prove its equivalence (in a certain sense) to the original problem. Then using the Fourier method, solving an equivalent problem is reduced to solving a system of integral equations and by the contraction mappings principle the existence and uniqueness theorem for auxiliary problem is proved. Further, on the basis of the equivalency of these problems the uniquely existence theorem for the classical solution of the considered inverse problem is proved and some considerations on the numerical solution for this inverse problem are presented with the examples.

scholarly journals On blowing-up solutions for multi-time nonlinear hyperbolic equations and systems

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2599-2609
Author(s):  
B. Ahmad ◽  
A. Alsaedi ◽  
E. Cuesta ◽  
M. Kirane
Keyword(s):  
Nonlinear Equation ◽  
Hyperbolic Equation ◽  
Space Dimension ◽  
Hyperbolic Equations ◽  
Nonlinear Hyperbolic Equation ◽  
Two Dimensional ◽  
Nonlinear Hyperbolic Equations ◽  
Blowing Up ◽  
Time Order ◽  
Blowing Up Solutions

For a two-dimensional time nonlinear hyperbolic equation with a power nonlinearity, a threshold exponent depending on the space dimension is presented. Furthermore, the analysis is extended not only to a system of two equations but also to a two-time fractional nonlinear equation with different time order derivatives.

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