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arXiv · 1805.09666

On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions

Piotr Kalita·Piotr Zgliczyński
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Abstract

We study the non-autonomously forced Burgers equation $$ u_t(x,t) + u(x,t)u_x(x,t) - u_{xx}(x,t) = f(x,t) $$ on the space interval $(0,1)$ with two sets of the boundary conditions: the Dirichlet and periodic ones. For both situations we prove that there exists the unique $H^1$ bounded trajectory of this equation defined for all $t\in \mathbb{R}$. Moreover we demonstrate that this trajectory attracts all trajectories both in pullback and forward sense. We also prove that for the Dirichlet case this attraction is exponential.

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Piotr Kalita, Piotr Zgliczyński. 2018-05-24. On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions. https://arxiv.org/abs/1805.09666

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