广义BBM-Burgers方程初边值问题的L2衰减估计
L2 Attenuation Estimation for the Initial Boundary Value Problem of the Generalized BBM-Burgers Equation
摘要: 本文主要研究如下本文研究的是广义BBM-Burgers方程扩散波的衰减估计问题，利用已经证明过的广义BBM-Burgers方程的解关于扩散波的渐近稳定，对该解进行衰减估计，并且在本文将证明广义BBM-Burgers方程解在L2范数下的衰减速度为(1t)−12。即对方程：{utf(u)x=uxxuxxtu(x,t)|t=0=u0(x),u(0,t)=u−在本文中我们将证明在波的强度δ:=|u−u−|及初值u0(x)适当小的情况下，广义BBM-Burgers方程的扰动方程形式的解的衰减速度为(1t)−12。
Abstract: This paper mainly studies as follows: This paper studies the attenuation estimation of the diffusion wave of the generalized BBM-Burgers equation. The solution of the generalized BBM-Burgers equation, which has been proved to be about the asymptotic stability of the diffusion wave, is used to estimate the attenuation of the solution. In this paper, it is proved that the decay rate of the solution of the generalized BBM-Burgers equation is(1t)−12under the L2 norm. Immediate pair equation:{utf(u)x=uxxuxxtu(x,t)|t=0=u0(x),u(0,t)=u−in this paper, we will prove that if the wave intensityδ:=|u−u−|and the initial valueu0(x)are appropriately small, the decay velocity of the perturbation equation of the generalized BBM-Burgers equation is(1t)−12.
文章引用：刘媛媛. 广义BBM-Burgers方程初边值问题的L2衰减估计[J]. 理论数学, 2024, 14(5): 351-356. https://doi.org/10.12677/pm.2024.145192

参考文献

[1] Benjamin, T.B., Bona, J.L. and Mahony, J.J. (1972) Model Equations for Long Waves in Nonlinear Dispersive Systems. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 272, 47-78. [Google Scholar] [CrossRef] 
[2] 徐红梅, 朱丽丽. 高维BBM-Burgers方程解的衰减估计[J]. 数学杂志, 2018, 38(6): 1049-1053.
[3] 余沛. 带有分数扩散的多维Burgers方程的衰减估计[J]. 数学物理学报, 2016, 36(2): 340-352.
[4] 易菊燕, 罗祠军, 陈诚. Kdv-Burgers方程初边值问题的LP-衰减估计[J]. 哈尔滨商业大学学报(自然科学版), 2012, 28(5): 609-615.
[5] 孙露露. 二维半空间上BBM-Burgers方程平面边界层解的稳定性及衰减估计[D]: [硕士学位论文]. 武汉: 华中科技大学, 2015.
[6] 王玮. 具有耗散项的广义BBM-Burgers方程的初值问题[D]: [硕士学位论文]. 郑州: 华北水利水电大学, 2014.
[7] 张卫国, 徐晋, 李想, 等. MKdV-Burgers方程衰减振荡解的近似解和误差估计[J]. 上海理工大学学报, 2012, 34(5): 409-418 490.
[8] 阮立志. 无粘性Burgers方程黎曼问题光滑近似解的高阶衰减估计[J]. 中南民族大学学报(自然科学版), 2006, 25(4): 97-100.
[9] 张能伟, 陈翔英. 一类广义BBM-Burgers方程的Cauchy问题[J]. 郑州大学学报(理学版), 2012, 44(2): 24-30.
[10] Gheraibia, B. and Boumaza, N. (2023) Initial Boundary Value Problem for a Viscoelastic Wave Equation with Balakrishnan—Taylor Damping and a Delay Term: Decay Estimates and Blow-Up Result. Boundary Value Problems, 2023, Article No. 93. [Google Scholar] [CrossRef] 
[11] Li, H., Li, J. and Zhang, J. (2023) Existence and Decay Estimates of Solution for a Fourth Order Quasi-Geostrophic Equation. Journal of Nonlinear Mathematical Physics, 30, 1282-1294. [Google Scholar] [CrossRef] 
[12] Fukuda, I. and Hirayama, H. (2023) Large Time Behavior and Optimal Decay Estimate for Solutions to the Generalized Kadomtsev-Petviashvili-Burgers Equation in 2D. Nonlinear Analysis, 234, Article 113322. [Google Scholar] [CrossRef] 
[13] Ma, C. (2023) Global Well-Posedness and Optimal Decay Estimate for the Incompressible Porous Medium Equation Near a Nontrivial Equilibrium. Applied Mathematics and Computation, 440, Article 127680. [Google Scholar] [CrossRef] 
[14] Kagei, Y. and Takeda, H. (2023) Decay Estimates of Solutions to Nonlinear Elastic Wave Equations with Viscoelastic Terms in the Framework of Lp-Sobolev Spaces. Journal of Mathematical Analysis and Applications, 519, Article 126801. [Google Scholar] [CrossRef] 
[15] Tong, L. (2024) Global Existence and Decay Estimates of the Classical Solution to the Compressible Navier-Stokes-Smoluchowski Equations in R3. Advances in Nonlinear Analysis, 13, 20230131. [Google Scholar] [CrossRef] 
[16] Miao, X., Zhao, J. and Chu, C. (2024) Sharp Decay Estimate for Solutions of General Choquard Equations. Bulletin des Sciences Mathématiques, 190, Article 103374. [Google Scholar] [CrossRef] 
[17] Taira, K. (2022) A Remark on Strichartz Estimates for Schrödinger Equations with Slowly Decaying Potentials. Proceedings of the American Mathematical Society, 150, 3953-3958. [Google Scholar] [CrossRef] 
[18] Bouclet, J.-M. and Burq, N. (2021) Sharp Resolvent and Time-Decay Estimates for Dispersive Equations on Asymptotically Euclidean Backgrounds. Duke Mathematical Journal, 170, 2575-2629. [Google Scholar] [CrossRef] 
[19] Berbiche, M. (2021) Energy Decay Estimates of Solutions for Viscoelastic Damped Wave Equations in Rn. Bulletin of the Malaysian Mathematical Sciences Society, 44, 3175-3214. [Google Scholar] [CrossRef] 
[20] Del Pezzo, L.M. and Quaas, A. (2020) Spectrum of the Fractional P-Laplacian in RN and Decay Estimate for Positive Solutions of a Schrödinger Equation. Nonlinear Analysis, 193, Article 111479.

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