Lyapunov Exponents for Burgers' Equation
Alexei Kourbatov
TL;DR
This paper analyzes the asymptotic behavior of solutions to the one-dimensional viscous Burgers' equation by establishing existence, uniqueness, stability, and explicit formulas for stationary solutions, along with Lyapunov exponents.
Contribution
It provides explicit formulas for solutions and analytically determines Lyapunov exponents for the Burgers' equation, advancing understanding of its long-term dynamics.
Findings
Existence and uniqueness of stationary solutions
Explicit formulas for solutions
Lyapunov exponents characterizing asymptotic behavior
Abstract
We establish the existence, uniqueness, and stability of the stationary solution of the one-dimensional viscous Burgers equation with the Dirichlet boundary conditions on a finite interval. We obtain explicit formulas for solutions and analytically determine the Lyapunov exponents characterizing the asymptotic behavior of arbitrary solutions approaching the stationary one.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Aquatic and Environmental Studies · Mathematical Biology Tumor Growth