Quasilinear parabolic equations with first order terms and L¹-data in moving domains

2020/02/28 by Đỗ Lân, Dang Thanh Son, Lan, Do +5 · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.00064

openalex publication_date 2020/02/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

The global existence of weak solutions to a class of quasilinear parabolic equations with nonlinearities depending on first order terms and integrable data in a moving domain is investigated. The class includes the p-Laplace equation as a special case. Weak solutions are shown to be global by obtaining appropriate estimates on the gradient as well as a suitable version of Aubin-Lions lemma in moving domains.

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• Global higher integrability for systems with p-growth structure in noncylindrical domains

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