分数阶 Burgers 方程时间周期弱解的唯一性与渐近稳定性

Abstract

Abstract:

The paper is concerned with the time-periodic (T-periodic) problem of fractional Burgers equation on the real line. Based on the Galerkin approximates and Fourier expansion, we first prove the existence of T-periodic solution to a linearized version. Then, the existence and uniqueness of T-periodic solution for the nonlinear equation are established by constructing a suitable contraction mapping. Furthermore, we show that the unique T-periodic solution is asymptotically stable. In addition, our method can be extended to the classical forced Burgers equation in a bounded region, which improves the known result.

Key words: Uniqueness, Fractional order, Contraction mapping, Asymptotic stability

CLC Number:

O175

Xu Fei, Zhang Yong. Uniqueness and Asymptotic Stability of Time-Periodic Solutions for the Fractional Burgers Equation[J].Acta mathematica scientia,Series A, 2023, 43(6): 1710-1722.

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Uniqueness and Asymptotic Stability of Time-Periodic Solutions for the Fractional Burgers Equation

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