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On a Nonlinear Wave Equation Associated with Dirichlet Conditions: Solvability and Asymptotic Expansion of Solutions in Many Small Parameters
並列摘要
A Dirichlet problem for a nonlinear wave equation is investigated. Under suitable assumptions, we prove the solvability and the uniqueness of a weak solution of the above problem. On the other hand, a high-order asymptotic expansion of a weak solution in many small parameters is studied. Our approach is based on the Faedo-Galerkin method, the compact imbedding theorems, and the Taylor expansion of a function.
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- Smarda, Z., & Rebenda, J. (2012). Asymptotic Behaviour of a Two-Dimensional Differential System with a Finite Number of Nonconstant Delays under the Conditions of Instability. Abstract and Applied Analysis, 2012(), 1453-1472-784. https://doi.org/10.1155/2012/952601
- Liu, Y., Zhao, H., & Yan, J. (2016). Existence of Nonoscillatory Solutions of Higher-Order Neutral Differential Equations with Distributed Coefficients and Delays. Discrete Dynamics in Nature and Society, 2016(), 12-18-001. https://doi.org/10.1155/2016/1026726
- Mei, S. L., Lv, H. L., & Ma, Q. (2008). Construction of Interval Wavelet Based on Restricted Variational Principle and Its Application for Solving Differential Equations. Mathematical Problems in Engineering, 2008(), 919-932. https://doi.org/10.1155/2008/629253
- Bachar, I., & Maagli, H. (2013). Existence and Uniqueness of Positive Solution for a Fractional Dirichlet Problem with Combined Nonlinear Effects in Bounded Domains. Abstract and Applied Analysis, 2013(), 86-94-309. https://doi.org/10.1155/2013/295480
- Liu, Y., Zhang, J., & Yan, J. (2013). Existence of Nonoscillatory Solutions for System of Higher-Order Neutral Differential Equations with Distributed Deviating Arguments. Discrete Dynamics in Nature and Society, 2013(), 733-740-086. https://doi.org/10.1155/2013/391973