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 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 REGULARITY OF SOLUTIONS TO A TIME-FRACTIONAL DIFFUSION EQUATION

2010 ◽  
Vol 52 (2) ◽  
pp. 123-138 ◽  
Author(s):  
WILLIAM MCLEAN
Keyword(s):  
Numerical Methods ◽  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Spatial Domain ◽  
Fractional Diffusion Equation ◽  
Regularity Of Solutions ◽  
Partial Derivatives ◽  
Classical Diffusion ◽  
Time Fractional Diffusion Equation ◽  
Derivatives Of

AbstractWe prove estimates for the partial derivatives of the solution to a time-fractional diffusion equation posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is typically less regular than in the familiar case of classical diffusion.

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.

Multi-focus image fusion based on depth extraction with inhomogeneous diffusion equation

2016 ◽  
Vol 125 ◽  
pp. 171-186 ◽  
Author(s):  
Jinsheng Xiao ◽  
Tingting Liu ◽  
Yongqin Zhang ◽  
Baiyu Zou ◽  
Junfeng Lei ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Image Fusion ◽  
Depth Extraction ◽  
Focus Image ◽  
Inhomogeneous Diffusion
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