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

Do Lan; Dang Thanh Son; Bao Quoc Tang; Le Thi Thuy

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

Analysis of PDEs 2020-12-18 v2

Authors: Do Lan , Dang Thanh Son , Bao Quoc Tang , Le Thi Thuy

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.

Keywords

quasilinear parabolic equations moving domains weak solutions first order terms l1-data aubin-lions lemma p-laplace equation

Cite

@article{arxiv.2003.00064,
  title  = {Quasilinear parabolic equations with first order terms and $L^1$-data in moving domains},
  author = {Do Lan and Dang Thanh Son and Bao Quoc Tang and Le Thi Thuy},
  journal= {arXiv preprint arXiv:2003.00064},
  year   = {2020}
}

Comments

accepted in Nonlinear Analysis (2020)

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