On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains
We study the existence and uniqueness of the positive solutions of the problem (P): Ә u - Δu + u = 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L (Ω), when Ω is a bounded domain in ℝ . We construct a maximal solution, prove that this maximal solution is a large solution whenever q...
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| Veröffentlicht in: | Advanced nonlinear studies 2009-02, Vol.9 (1), p.149-164 |
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| container_title | Advanced nonlinear studies |
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| creator | Al Sayed, Waad Véron, Laurent |
| description | We study the existence and uniqueness of the positive solutions of the problem (P): Ә
u - Δu + u
= 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L
(Ω), when Ω is a bounded domain in ℝ
. We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N - 2) and it is unique if ӘΩ = ӘΩ̅
. If ӘΩ has the local graph property, we prove that there exists at most one solution to problem (P). |
| doi_str_mv | 10.1515/ans-2009-0107 |
| format | Article |
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u - Δu + u
= 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L
(Ω), when Ω is a bounded domain in ℝ
. We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N - 2) and it is unique if ӘΩ = ӘΩ̅
. If ӘΩ has the local graph property, we prove that there exists at most one solution to problem (P).</description><identifier>ISSN: 1536-1365</identifier><identifier>EISSN: 2169-0375</identifier><identifier>DOI: 10.1515/ans-2009-0107</identifier><language>eng</language><publisher>Advanced Nonlinear Studies, Inc</publisher><subject>Analysis of PDEs ; Mathematics ; Parabolic equations ; removable singularities ; self-similarity ; singular solutions</subject><ispartof>Advanced nonlinear studies, 2009-02, Vol.9 (1), p.149-164</ispartof><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c361t-f2492b469d061c88f956a17e26367788a5de130a0c5dc71aa15d3148f0aaa9373</citedby><cites>FETCH-LOGICAL-c361t-f2492b469d061c88f956a17e26367788a5de130a0c5dc71aa15d3148f0aaa9373</cites><orcidid>0000-0003-1190-9714</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.degruyter.com/document/doi/10.1515/ans-2009-0107/pdf$$EPDF$$P50$$Gwalterdegruyter$$H</linktopdf><linktohtml>$$Uhttps://www.degruyter.com/document/doi/10.1515/ans-2009-0107/html$$EHTML$$P50$$Gwalterdegruyter$$H</linktohtml><link.rule.ids>230,314,776,780,881,27901,27902,66901,68685</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00300801$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Al Sayed, Waad</creatorcontrib><creatorcontrib>Véron, Laurent</creatorcontrib><title>On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains</title><title>Advanced nonlinear studies</title><description>We study the existence and uniqueness of the positive solutions of the problem (P): Ә
u - Δu + u
= 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L
(Ω), when Ω is a bounded domain in ℝ
. We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N - 2) and it is unique if ӘΩ = ӘΩ̅
. If ӘΩ has the local graph property, we prove that there exists at most one solution to problem (P).</description><subject>Analysis of PDEs</subject><subject>Mathematics</subject><subject>Parabolic equations</subject><subject>removable singularities</subject><subject>self-similarity</subject><subject>singular solutions</subject><issn>1536-1365</issn><issn>2169-0375</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2009</creationdate><recordtype>article</recordtype><recordid>eNptkDFPwzAQhS0EEhV0ZM_KEPDFsZOwVaVQpIgiQVmta-K0rlKb2g2o_x6HICZuudPT9053j5AroDfAgd-i8XFCaRFToNkJGSUgwswyfkpGwJmIgQl-Tsbeb2motEhSzkfkfWGipdH7ThnlfWSbqES3VtGrbbuDtuZHeram1Uahi17Q4cq2uopm-w4HQJse8DtrD5vo3u5QG39JzhpsvRr_9guyfJi9TedxuXh8mk7KuGICDnGThDtWqShqKqDK86bgAiFTiWAiy_Icea2AUaQVr6sMEIHXDNK8oYhYsIxdkOth7wZb-eH0Dt1RWtRyPillr1HKKM0pfCaBjQe2ctZ7p5o_A1DZZyhDhrLPUPYZBv5u4L-wPShXq7XrjmGQW9s5E77631cApAX7BpIUdsA</recordid><startdate>20090201</startdate><enddate>20090201</enddate><creator>Al Sayed, Waad</creator><creator>Véron, Laurent</creator><general>Advanced Nonlinear Studies, Inc</general><general>Walter de Gruyter GmbH</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0003-1190-9714</orcidid></search><sort><creationdate>20090201</creationdate><title>On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains</title><author>Al Sayed, Waad ; Véron, Laurent</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c361t-f2492b469d061c88f956a17e26367788a5de130a0c5dc71aa15d3148f0aaa9373</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2009</creationdate><topic>Analysis of PDEs</topic><topic>Mathematics</topic><topic>Parabolic equations</topic><topic>removable singularities</topic><topic>self-similarity</topic><topic>singular solutions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Al Sayed, Waad</creatorcontrib><creatorcontrib>Véron, Laurent</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Advanced nonlinear studies</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Al Sayed, Waad</au><au>Véron, Laurent</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains</atitle><jtitle>Advanced nonlinear studies</jtitle><date>2009-02-01</date><risdate>2009</risdate><volume>9</volume><issue>1</issue><spage>149</spage><epage>164</epage><pages>149-164</pages><issn>1536-1365</issn><eissn>2169-0375</eissn><abstract>We study the existence and uniqueness of the positive solutions of the problem (P): Ә
u - Δu + u
= 0 (q > 1) in Ω × (0, ∞), u = ∞ on ӘΩ × (0, ∞) and u(., 0) ∈ L
(Ω), when Ω is a bounded domain in ℝ
. We construct a maximal solution, prove that this maximal solution is a large solution whenever q < N/(N - 2) and it is unique if ӘΩ = ӘΩ̅
. If ӘΩ has the local graph property, we prove that there exists at most one solution to problem (P).</abstract><pub>Advanced Nonlinear Studies, Inc</pub><doi>10.1515/ans-2009-0107</doi><tpages>16</tpages><orcidid>https://orcid.org/0000-0003-1190-9714</orcidid><oa>free_for_read</oa></addata></record> |
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| ispartof | Advanced nonlinear studies, 2009-02, Vol.9 (1), p.149-164 |
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| language | eng |
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| source | Alma/SFX Local Collection; Walter De Gruyter: Open Access Journals |
| subjects | Analysis of PDEs Mathematics Parabolic equations removable singularities self-similarity singular solutions |
| title | On Uniqueness of Large Solutions of Nonlinear Parabolic Equations in Nonsmooth Domains |
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