scholarly journals On the Stability of Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Soon-Mo Jung
Keyword(s):  
Wave Equation ◽  
Ulam Stability ◽  
Differentiable Functions ◽  
The Stability

We prove the generalized Hyers-Ulam stability of the wave equation,Δu=(1/c2)utt, in a class of twice continuously differentiable functions under some conditions.

scholarly journals On the Stability of One-Dimensional Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Soon-Mo Jung
Keyword(s):  
Wave Equation ◽  
Ulam Stability ◽  
One Dimensional ◽  
Differentiable Functions ◽  
The Stability ◽  
The One ◽  
Dimensional Wave

We prove the generalized Hyers-Ulam stability of the one-dimensional wave equation,utt=c2uxx, in a class of twice continuously differentiable functions.

scholarly journals On the Stability of Heat Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Balázs Hegyi ◽  
Soon-Mo Jung
Keyword(s):  
Heat Equation ◽  
Ulam Stability ◽  
Differentiable Functions ◽  
The Stability

We prove the generalized Hyers-Ulam stability of the heat equation, , in a class of twice continuously differentiable functions under certain conditions.

scholarly journals A Fixed Point Approach to the Stability of an Integral Equation Related to the Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Soon-Mo Jung
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Method ◽  
Point Method ◽  
Ulam Stability ◽  
Fixed Point Approach ◽  
The Stability

We will apply the fixed point method for proving the generalized Hyers-Ulam stability of the integral equation1/2c∫x-ctx+ctuτ,t0dτ=ux,twhich is strongly related to the wave equation.

scholarly journals An Operator Method for the Stability of Inhomogeneous Wave Equations

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 324 ◽  
Author(s):  
Ginkyu Choi ◽  
Soon-Mo Jung ◽  
Jaiok Roh
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Operator Method ◽  
Ulam Stability ◽  
Inhomogeneous Wave ◽  
Partial Derivatives ◽  
The Stability

In this paper, we will apply the operator method to prove the generalized Hyers-Ulam stability of the wave equation, u t t ( x , t ) − c 2 ▵ u ( x , t ) = f ( x , t ) , for a class of real-valued functions with continuous second partial derivatives. Finally, we will discuss the stability more explicitly by giving examples.

scholarly journals A Dilation Invariance Method and the Stability of Inhomogeneous Wave Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 70 ◽  
Author(s):  
Ginkyu Choi ◽  
Soon-Mo Jung
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Ulam Stability ◽  
Inhomogeneous Wave ◽  
Partial Derivatives ◽  
Inhomogeneous Wave Equation ◽  
Time Variables ◽  
The Stability

We apply the method of a kind of dilation invariance to prove the generalized Hyers-Ulam stability of the (inhomogeneous) wave equation with a source, u t t ( x , t ) − c 2 ▵ u ( x , t ) = f ( x , t ) , for a class of real-valued functions with continuous second partial derivatives in each of spatial and the time variables.

On the stability of a nonic functional equation in quasi-normed spaces

2016 ◽  
Vol 12 (3) ◽  
pp. 4368-4374
Author(s):  
Soo Hwan Kim
Keyword(s):  
Functional Equation ◽  
Ulam Stability ◽  
Normed Spaces ◽  
The Stability

In this paper, we extend normed spaces to quasi-normed spaces and prove the generalized Hyers-Ulam stability of a nonic functional equation:$$\aligned&f(x+5y) - 9f(x+4y) + 36f(x+3y) - 84f(x+2y) + 126f(x+y) - 126f(x)\\&\qquad + 84f(x-y)-36f(x-2y)+9f(x-3y)-f(x-4y) = 9 ! f(y),\endaligned$$where $9 ! = 362880$ in quasi-normed spaces.

scholarly journals The new investigation of the stability of mixed type additive-quartic functional equations in non-Archimedean spaces

2020 ◽  
Vol 53 (1) ◽  
pp. 174-192
Author(s):  
Anurak Thanyacharoen ◽  
Wutiphol Sintunavarat
Keyword(s):  
Functional Equation ◽  
Normed Space ◽  
Functional Equations ◽  
Mixed Type ◽  
Additive Group ◽  
Ulam Stability ◽  
Quartic Functional Equation ◽  
The Stability

AbstractIn this article, we prove the generalized Hyers-Ulam stability for the following additive-quartic functional equation:f(x+3y)+f(x-3y)+f(x+2y)+f(x-2y)+22f(x)+24f(y)=13{[}f(x+y)+f(x-y)]+12f(2y),where f maps from an additive group to a complete non-Archimedean normed space.

scholarly journals Some arguments for the wave equation in Quantum theory

2021 ◽  
Vol 5 (1) ◽  
pp. 314-336
Author(s):  
Tristram de Piro ◽  
Keyword(s):  
Electromagnetic Field ◽  
Wave Equation ◽  
Quantum Theory ◽  
Continuity Equation ◽  
Wave Equations ◽  
Maxwell's Equations ◽  
Atomic System ◽  
Balmer Series ◽  
Inertial Frames ◽  
The Stability

We clarify some arguments concerning Jefimenko’s equations, as a way of constructing solutions to Maxwell’s equations, for charge and current satisfying the continuity equation. We then isolate a condition on non-radiation in all inertial frames, which is intuitively reasonable for the stability of an atomic system, and prove that the condition is equivalent to the charge and current satisfying certain relations, including the wave equations. Finally, we prove that with these relations, the energy in the electromagnetic field is quantised and displays the properties of the Balmer series.

scholarly journals Boundary Stabilization of a Semilinear Wave Equation with Variable Coefficients under the Time-Varying and Nonlinear Feedback

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bei Gong ◽  
Xiaopeng Zhao
Keyword(s):  
Wave Equation ◽  
Riemannian Geometry ◽  
Nonlinear Term ◽  
Variable Coefficients ◽  
Time Varying ◽  
Nonlinear Feedback ◽  
Boundary Stabilization ◽  
Semilinear Wave Equation ◽  
The Stability ◽  
Stability Results

We study the boundary stabilization of a semilinear wave equation with variable coefficients under the time-varying and nonlinear feedback. By the Riemannian geometry methods, we obtain the stability results of the system under suitable assumptions of the bound of the time-varying term and the nonlinearity of the nonlinear term.

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