Existence and uniqueness for the inhomogeneous 1-Laplace evolution equation revisited

2022/03/23 by Marta Latorre, Latorre, Marta, Sergio Segura de León +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.12571

openalex publication_date 2022/03/23 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper we deal with an inhomogeneous parabolic Dirichlet problem involving the 1-Laplacian operator. We show the existence of a unique solution when data belong to L¹(0,T;L²(Ω)) for every T>0. As a consequence, global existence and uniqueness for data in L¹_loc(0,+∞;L²(Ω)) is obtained. Our analysis retrieves the results of \citeSW in a correct and complete way.

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