On the L₁--stability for parabolic equations with a supercritical drift term

2024/11/06 by Mikhail Glazkov, Glazkov, Mikhail, Timofey Shilkin +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2411.03816

openalex publication_date 2024/11/06 · openalex created_date 2024/11/15 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate the existence, uniqueness and stability of weak solutions of the initial boundary value problem with the Dirichlet boundary conditions for a parabolic equation with a drift b∈ L₂. We prove L₁-stability of solutions with respect to perturbations of the drift b in L₂ in the case if the drift satisfies the ``non-spectral'' condition div b≤ 0.

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