2023/11/20 by Ana Djurdjevac, Djurdjevac, Ana, Armen Shirikyan +1
Computer Science · Engineering · Physics and Astronomy · #35B35 #35K58 #60G10 #93D23 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2311.12008
openalex publication_date 2023/11/20 · openalex created_date 2023/11/23 · openalex updated_date 2026/07/28
The paper deals with the problem of stability for the flow of the 1D Burgers equation on a circle. Using some ideas from the theory of positivity preserving semigroups, we establish the strong contraction in the L1 norm. As a consequence, it is proved that the equation with a bounded external force possesses a unique bounded solution on \mathbb R, which is exponentially stable in H1 as t→+∞. In the case of a random external force, we show that the difference between two trajectories goes to zero with probability 1.