scholarly journals Stability of the Wave Equation with a Source

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Soon-Mo Jung ◽  
Seungwook Min
Keyword(s):  
Wave Equation ◽  
Ulam Stability ◽  
Partial Derivatives

We prove the generalized Hyers-Ulam stability of the wave equation with a source, uttx,t-c2uxxx,t=fx,t, for a class of real-valued functions with continuous second partial derivatives in x and t.

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.

scholarly journals Stability of the Diffusion Equation with a Source

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Soon-Mo Jung ◽  
Seungwook Min
Keyword(s):  
Diffusion Equation ◽  
Ulam Stability ◽  
Partial Derivatives ◽  
Inhomogeneous Diffusion

We will prove the generalized Hyers-Ulam stability of the (inhomogeneous) diffusion equation with a source, ut(x,t)-k△u(x,t)=f(x,t), for a class of scalar functions with continuous second partial derivatives.

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 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 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.

On the motion of comet P/d’Arrest

1974 ◽  
Vol 22 ◽  
pp. 145-148
Author(s):  
W. J. Klepczynski
Keyword(s):  
Equations Of Motion ◽  
Variational Equations ◽  
Partial Derivatives

AbstractThe differences between numerically approximated partial derivatives and partial derivatives obtained by integrating the variational equations are computed for Comet P/d’Arrest. The effect of errors in the IAU adopted system of masses, normally used in the integration of the equations of motion of comets of this type, is investigated. It is concluded that the resulting effects are negligible when compared with the observed discrepancies in the motion of this comet.

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