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Exponential stability of the flow for a generalized Burgers equation on a circle

2023; Peoples' Friendship University of Russia; Volume: 69; Issue: 4 Linguagem: Inglês

10.22363/2413-3639-2023-69-4-588-598

2949-0618

Ana Djurdjevac, Armen Shirikyan,

Advanced Mathematical Physics Problems

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 \(L^1\) norm. As a consequence, it is proved that the equation with a bounded external force possesses a unique bounded solution on\(R\), which is exponentially stable in\(H^1\) as \(t\to+\infty\). In the case of a random external force, we show that the difference between two trajectories goes to zero with probability\(1\).