# Uniqueness and asymptotic stability of time-periodic solution for the fractal Burgers equation

@inproceedings{Zhang2021UniquenessAA, title={Uniqueness and asymptotic stability of time-periodic solution for the fractal Burgers equation}, author={Yong Zhang}, year={2021} }

Abstract. The paper is concerned with the time-periodic (T-periodic) problem of the fractal Burgers equation with a T-periodic force on the real line. Based on the Galerkin approximates and Fourier series (transform) methods, we first prove the existence of T-periodic solution to a linearized version. Then, the existence and uniqueness of T-periodic solution to the nonlinear equation are established by the contraction mapping argument. Furthermore, we show that the unique T-periodic solution is…

## One Citation

Uniqueness and stability of steady-state solution with finite energy to the fractal Burgers equation

- Mathematics
- 2021

The paper is concerned with the steady-state Burgers equation of fractional dissipation on the real line. We first prove the global existence of viscosity weak solutions to the fractal Burgers…

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