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On nonlinear parabolic equations with singular lower order term
In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is ∂ u ∂ t - div ( ( a ( x , t ) + | u | q ) ∇ u ) = f u γ in Q , u ( x , t ) = 0 on Γ , u ( x , 0 ) = u 0 ( x ) in Ω , where Ω is a bounded open subset of R N , N ≥ 2 , Q is...
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| Published in: | Journal of elliptic and parabolic equations 2022-06, Vol.8 (1), p.49-75 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c291t-d75ad3c91678d87457dfbb59e3374d0ded6cef646017814d067a5a6c35ad38853 |
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| cites | cdi_FETCH-LOGICAL-c291t-d75ad3c91678d87457dfbb59e3374d0ded6cef646017814d067a5a6c35ad38853 |
| container_end_page | 75 |
| container_issue | 1 |
| container_start_page | 49 |
| container_title | Journal of elliptic and parabolic equations |
| container_volume | 8 |
| creator | El hadfi, Youssef El ouardy, Mounim Ifzarne, Aziz Sbai, Abdelaaziz |
| description | In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is
∂
u
∂
t
-
div
(
(
a
(
x
,
t
)
+
|
u
|
q
)
∇
u
)
=
f
u
γ
in
Q
,
u
(
x
,
t
)
=
0
on
Γ
,
u
(
x
,
0
)
=
u
0
(
x
)
in
Ω
,
where
Ω
is a bounded open subset of
R
N
,
N
≥
2
,
Q
is the cylinder
Ω
×
(
0
,
T
)
,
T
>
0
,
Γ
the lateral surface
∂
Ω
×
(
0
,
T
)
,
q
>
0
,
γ
>
0
,
and
f
is non-negative function belonging to some Lebesgue space
L
m
(
Q
)
,
m
≥
1
and
u
0
∈
L
∞
(
Ω
)
such that
∀
ω
⊂
⊂
Ω
,
∃
D
ω
>
0
:
u
0
≥
D
ω
in
ω
. |
| doi_str_mv | 10.1007/s41808-021-00138-5 |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s41808_021_00138_5</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s41808_021_00138_5</sourcerecordid><originalsourceid>FETCH-LOGICAL-c291t-d75ad3c91678d87457dfbb59e3374d0ded6cef646017814d067a5a6c35ad38853</originalsourceid><addsrcrecordid>eNp9kE1LxDAQhoMouKz7Bzz1D0QnSfPRk8jix8LCXvQc0iZds3STNWlZ_Pe2Vjx6mRmG9xmGB6FbAncEQN7nkihQGCjBAIQpzC_QgtJK4ApYdfk3U7hGq5wPAEAlK6WABXrYhSLE0PngTCpOJpk6dr4p3Odgeh9DLs6-_yiyD_uhGxNdPLtUxGTH2rt0vEFXremyW_32JXp_fnpbv-Lt7mWzftzihlakx1ZyY1lTESGVVbLk0rZ1zSvHmCwtWGdF41pRCiBSkXEjpOFGNGzClOJsieh8t0kx5-RafUr-aNKXJqAnC3q2oEcL-seCniA2Q3kMh71L-hCHFMY__6O-AUbgX9U</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On nonlinear parabolic equations with singular lower order term</title><source>Springer Link</source><creator>El hadfi, Youssef ; El ouardy, Mounim ; Ifzarne, Aziz ; Sbai, Abdelaaziz</creator><creatorcontrib>El hadfi, Youssef ; El ouardy, Mounim ; Ifzarne, Aziz ; Sbai, Abdelaaziz</creatorcontrib><description>In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is
∂
u
∂
t
-
div
(
(
a
(
x
,
t
)
+
|
u
|
q
)
∇
u
)
=
f
u
γ
in
Q
,
u
(
x
,
t
)
=
0
on
Γ
,
u
(
x
,
0
)
=
u
0
(
x
)
in
Ω
,
where
Ω
is a bounded open subset of
R
N
,
N
≥
2
,
Q
is the cylinder
Ω
×
(
0
,
T
)
,
T
>
0
,
Γ
the lateral surface
∂
Ω
×
(
0
,
T
)
,
q
>
0
,
γ
>
0
,
and
f
is non-negative function belonging to some Lebesgue space
L
m
(
Q
)
,
m
≥
1
and
u
0
∈
L
∞
(
Ω
)
such that
∀
ω
⊂
⊂
Ω
,
∃
D
ω
>
0
:
u
0
≥
D
ω
in
ω
.</description><identifier>ISSN: 2296-9020</identifier><identifier>EISSN: 2296-9039</identifier><identifier>DOI: 10.1007/s41808-021-00138-5</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics ; Partial Differential Equations</subject><ispartof>Journal of elliptic and parabolic equations, 2022-06, Vol.8 (1), p.49-75</ispartof><rights>Orthogonal Publisher and Springer Nature Switzerland AG 2021</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c291t-d75ad3c91678d87457dfbb59e3374d0ded6cef646017814d067a5a6c35ad38853</citedby><cites>FETCH-LOGICAL-c291t-d75ad3c91678d87457dfbb59e3374d0ded6cef646017814d067a5a6c35ad38853</cites><orcidid>0000-0003-4483-2709</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>El hadfi, Youssef</creatorcontrib><creatorcontrib>El ouardy, Mounim</creatorcontrib><creatorcontrib>Ifzarne, Aziz</creatorcontrib><creatorcontrib>Sbai, Abdelaaziz</creatorcontrib><title>On nonlinear parabolic equations with singular lower order term</title><title>Journal of elliptic and parabolic equations</title><addtitle>J Elliptic Parabol Equ</addtitle><description>In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is
∂
u
∂
t
-
div
(
(
a
(
x
,
t
)
+
|
u
|
q
)
∇
u
)
=
f
u
γ
in
Q
,
u
(
x
,
t
)
=
0
on
Γ
,
u
(
x
,
0
)
=
u
0
(
x
)
in
Ω
,
where
Ω
is a bounded open subset of
R
N
,
N
≥
2
,
Q
is the cylinder
Ω
×
(
0
,
T
)
,
T
>
0
,
Γ
the lateral surface
∂
Ω
×
(
0
,
T
)
,
q
>
0
,
γ
>
0
,
and
f
is non-negative function belonging to some Lebesgue space
L
m
(
Q
)
,
m
≥
1
and
u
0
∈
L
∞
(
Ω
)
such that
∀
ω
⊂
⊂
Ω
,
∃
D
ω
>
0
:
u
0
≥
D
ω
in
ω
.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><issn>2296-9020</issn><issn>2296-9039</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouKz7Bzz1D0QnSfPRk8jix8LCXvQc0iZds3STNWlZ_Pe2Vjx6mRmG9xmGB6FbAncEQN7nkihQGCjBAIQpzC_QgtJK4ApYdfk3U7hGq5wPAEAlK6WABXrYhSLE0PngTCpOJpk6dr4p3Odgeh9DLs6-_yiyD_uhGxNdPLtUxGTH2rt0vEFXremyW_32JXp_fnpbv-Lt7mWzftzihlakx1ZyY1lTESGVVbLk0rZ1zSvHmCwtWGdF41pRCiBSkXEjpOFGNGzClOJsieh8t0kx5-RafUr-aNKXJqAnC3q2oEcL-seCniA2Q3kMh71L-hCHFMY__6O-AUbgX9U</recordid><startdate>202206</startdate><enddate>202206</enddate><creator>El hadfi, Youssef</creator><creator>El ouardy, Mounim</creator><creator>Ifzarne, Aziz</creator><creator>Sbai, Abdelaaziz</creator><general>Springer International Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4483-2709</orcidid></search><sort><creationdate>202206</creationdate><title>On nonlinear parabolic equations with singular lower order term</title><author>El hadfi, Youssef ; El ouardy, Mounim ; Ifzarne, Aziz ; Sbai, Abdelaaziz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c291t-d75ad3c91678d87457dfbb59e3374d0ded6cef646017814d067a5a6c35ad38853</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>El hadfi, Youssef</creatorcontrib><creatorcontrib>El ouardy, Mounim</creatorcontrib><creatorcontrib>Ifzarne, Aziz</creatorcontrib><creatorcontrib>Sbai, Abdelaaziz</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of elliptic and parabolic equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>El hadfi, Youssef</au><au>El ouardy, Mounim</au><au>Ifzarne, Aziz</au><au>Sbai, Abdelaaziz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On nonlinear parabolic equations with singular lower order term</atitle><jtitle>Journal of elliptic and parabolic equations</jtitle><stitle>J Elliptic Parabol Equ</stitle><date>2022-06</date><risdate>2022</risdate><volume>8</volume><issue>1</issue><spage>49</spage><epage>75</epage><pages>49-75</pages><issn>2296-9020</issn><eissn>2296-9039</eissn><abstract>In this paper we study existence and regularity results for solution to a nonlinear and singular parabolic problem. The model is
∂
u
∂
t
-
div
(
(
a
(
x
,
t
)
+
|
u
|
q
)
∇
u
)
=
f
u
γ
in
Q
,
u
(
x
,
t
)
=
0
on
Γ
,
u
(
x
,
0
)
=
u
0
(
x
)
in
Ω
,
where
Ω
is a bounded open subset of
R
N
,
N
≥
2
,
Q
is the cylinder
Ω
×
(
0
,
T
)
,
T
>
0
,
Γ
the lateral surface
∂
Ω
×
(
0
,
T
)
,
q
>
0
,
γ
>
0
,
and
f
is non-negative function belonging to some Lebesgue space
L
m
(
Q
)
,
m
≥
1
and
u
0
∈
L
∞
(
Ω
)
such that
∀
ω
⊂
⊂
Ω
,
∃
D
ω
>
0
:
u
0
≥
D
ω
in
ω
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s41808-021-00138-5</doi><tpages>27</tpages><orcidid>https://orcid.org/0000-0003-4483-2709</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 2296-9020 |
| ispartof | Journal of elliptic and parabolic equations, 2022-06, Vol.8 (1), p.49-75 |
| issn | 2296-9020 2296-9039 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s41808_021_00138_5 |
| source | Springer Link |
| subjects | Mathematics Mathematics and Statistics Partial Differential Equations |
| title | On nonlinear parabolic equations with singular lower order term |
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