The Well-Posedness of the Solutions Based on the L1 Initial Value Condition

The Well-Posedness of the Solutions Based on the L1 Initial Value Condition

The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value co...

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Bibliographic Details
Main Authors: Huashui Zhan, Zhen Zhou
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2018/6525637
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spelling doaj-59a52414b736474f859709c417b551982020-11-24T21:14:26ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/65256376525637The Well-Posedness of the Solutions Based on the L1 Initial Value ConditionHuashui Zhan0Zhen Zhou1School of Applied Mathematics, Xiamen University of Technology, Xiamen 361024, ChinaSchool of Science, Jimei University, Xiamen 361021, ChinaThe non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.http://dx.doi.org/10.1155/2018/6525637
collection DOAJ
language English
format Article
sources DOAJ
author Huashui Zhan
Zhen Zhou
spellingShingle Huashui Zhan
Zhen Zhou
The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
Journal of Function Spaces
author_facet Huashui Zhan
Zhen Zhou
author_sort Huashui Zhan
title The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
title_short The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
title_full The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
title_fullStr The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
title_full_unstemmed The Well-Posedness of the Solutions Based on the L1 Initial Value Condition
title_sort well-posedness of the solutions based on the l1 initial value condition
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8896
2314-8888
publishDate 2018-01-01
description The non-Newtonian polytropic filtration equation ut=div(a(x)|∇um|p-2∇um) is considered. Only if u0(x)∈L1(Ω), the well-posedness of solutions is studied. If the diffusion coefficient is degenerate on the boundary, then stability of the weak solutions is proved only depending upon the initial value conditions.
url http://dx.doi.org/10.1155/2018/6525637
work_keys_str_mv AT huashuizhan thewellposednessofthesolutionsbasedonthel1initialvaluecondition
AT zhenzhou thewellposednessofthesolutionsbasedonthel1initialvaluecondition
AT huashuizhan wellposednessofthesolutionsbasedonthel1initialvaluecondition
AT zhenzhou wellposednessofthesolutionsbasedonthel1initialvaluecondition
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