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On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 150 / Issue 4 / August 2020
- Published online by Cambridge University Press:
- 14 March 2019, pp. 2025-2054
- Print publication:
- August 2020
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- Article
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We study the non-autonomously forced Burgers equation
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 H1 bounded trajectory of this equation defined for all t ∈ 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.
$$u_t(x,t) + u(x,t)u_x(x,t)-u_{xx}(x,t) = f(x,t)$$
