Existence and uniqueness of weak solutions to a parabolic nonlocal 1-Laplacian equation

2024/06/27 by Dingding Li, Chao Zhang, Li, Dingding +1
Mathematics · Computer Science · Engineering · #Differential Equations and Boundary Problems #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2406.19020

Abstract

We consider a class of parabolic nonlocal 1-Laplacian equation u_t+(-Δ)^s₁u=f in Ω×(0,T]. By employing the Rothe time-discretization method, we establish the existence and uniqueness of weak solutions to the equation above. In particular, different from the previous results on the local case, we infer that the weak solution maintains (1)/(2)-Hölder continuity in time.

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