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On the stability of one-dimensional wave equation
1Mathematics Section, College of Science and Technology, Hongik University, Sejong 339-701, Republic of Korea.
Thescientificworldjournal
|November 30, 2013
Summary
This study proves the generalized Hyers-Ulam stability for the one-dimensional wave equation. The findings apply to functions that are twice continuously differentiable.
Area of Science:
- Differential Equations
- Functional Analysis
- Mathematical Physics
Background:
- The Hyers-Ulam stability concept addresses the resilience of solutions to differential equations under perturbations.
- The one-dimensional wave equation, u(tt) = c(2)u(xx), is a fundamental model in physics and engineering.
Purpose of the Study:
- To establish the generalized Hyers-Ulam stability of the one-dimensional wave equation.
- To analyze the stability within the specific domain of twice continuously differentiable functions.
Main Methods:
- Employing techniques from functional analysis.
- Applying methods to demonstrate stability for the specified wave equation.
Main Results:
- The generalized Hyers-Ulam stability of the one-dimensional wave equation is proven.
- The stability is confirmed for the class of twice continuously differentiable functions.
Conclusions:
- The results contribute to the understanding of the robustness of solutions for the wave equation.
- This stability analysis is crucial for numerical approximations and theoretical applications.
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