分数阶强阻尼波动方程的Fourier正则化
Fourier Regularization of Fractional Strongly Damped Wave Equations
摘要: 通过谱分解的方法研究了高斯白噪声扰动下分数阶强阻尼波动方程的终边值问题，这类问题是不适定的，即解不连续依赖于终值条件，应用Fourier截断方法建立了问题的正则解，并给出正则解和精确解间的收敛性误差估计，这说明了正则化方法的有效性。
Abstract: In this paper, by using spectral decomposition method, we study a final-boundary value problem of the fractional strongly damped wave equations with Gauss white noise. This problem is ill-posed in the sense of Hadamard, i.e. the solution discontinuity depends on the final condition. Hence, regularized solution is established by the Fourier truncation method. Moreover, we show the convergent error estimates between the regularized solution and the exact solution, which implies the regularized method is effective.
文章引用：容伟杰. 分数阶强阻尼波动方程的Fourier正则化[J]. 应用数学进展, 2022, 11(3): 1013-1020. https://doi.org/10.12677/AAM.2022.113109

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