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The global existence of weak solutions to a class of quasilinear parabolicequations with nonlinearities depending on first order terms and integrabledata in a moving domain is investigated. The class includes the $p$-Laplaceequation as a special case. Weak solutions are shown to be global by obtainingappropriate estimates on the gradient as well as a suitable version ofAubin-Lions lemma in moving domains.

Quasilinear parabolic equations with first order terms and $L^1$-data in moving domains