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The well-posedness of renormalized solutions for a non-uniformly parabolic equation


Authors: Chao Zhang and Shulin Zhou
Journal: Proc. Amer. Math. Soc. 145 (2017), 2577-2589
MSC (2010): Primary 35D05; Secondary 35D10
DOI: https://doi.org/10.1090/proc/13406
Published electronically: November 30, 2016
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Abstract: In this paper we present a unified approach to establish the existence of renormalized solutions and a comparison result for a class of non-uniformly parabolic initial-boundary value problems. As a consequence, the uniqueness of renormalized solutions and the equivalence between entropy and renormalized solutions for such equations are obtained. The results extend the well-posedness results for the classical $ p$-Laplacian type equations to a larger class of non-linear elliptic and parabolic PDEs including the nearly linear growth operators.


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Additional Information

Chao Zhang
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
Email: czhangmath@hit.edu.cn

Shulin Zhou
Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: szhou@math.pku.edu.cn

DOI: https://doi.org/10.1090/proc/13406
Keywords: Renormalized solutions, existence, uniqueness, parabolic
Received by editor(s): February 6, 2016
Received by editor(s) in revised form: July 27, 2016
Published electronically: November 30, 2016
Communicated by: Joachim Krieger
Article copyright: © Copyright 2016 American Mathematical Society

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