The well-posedness of renormalized solutions for a non-uniformly parabolic equation
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- by Chao Zhang and Shulin Zhou PDF
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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.References
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Additional Information
- Chao Zhang
- Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, People’s Republic of China
- MR Author ID: 889177
- Email: czhangmath@hit.edu.cn
- Shulin Zhou
- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 339831
- Email: szhou@math.pku.edu.cn
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 2577-2589
- MSC (2010): Primary 35D05; Secondary 35D10
- DOI: https://doi.org/10.1090/proc/13406
- MathSciNet review: 3626513