Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in R^sup N
We consider asymptotic behavior for a parabolic equation (p-heat equation) with (sub-)critical Sobolev and Hardy exponent potential ... where 1 < p < N, (N ≥ 2). If V(x) ≡ λ and s = q = p, it is shown by Azorero and Alonso (1998) that the solution for such Cauchy problem depends strongly on an...
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| Veröffentlicht in: | Nonlinear analysis: real world applications 2018-08, Vol.42, p.290 |
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| description | We consider asymptotic behavior for a parabolic equation (p-heat equation) with (sub-)critical Sobolev and Hardy exponent potential ... where 1 < p < N, (N ≥ 2). If V(x) ≡ λ and s = q = p, it is shown by Azorero and Alonso (1998) that the solution for such Cauchy problem depends strongly on and the best constant λN,p in Hardy’s inequality, specifically, the local or global solutions for this problem depend on the different cases of 1 < p < 2, p ≥ 2 and λ > λN,p, λ < λN,p. By using the standard domain expansion technique and some convenient integrability conditions on the weighted function V(x), we first establish that the Cauchy problem has at least one global solution for every 1 < p < N. We then apply the theory of multivalued semigroups or multivalued semiflows to get L2 (ℝN) global attractor for the p-heat equation with 2 ≤ p < N. Furthermore, the global attractor also belongs to L2 (ℝN) ∩ Lα (ℝN) when is suitably large. ProQuest: ... denotes formulae omitted. |
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If V(x) ≡ λ and s = q = p, it is shown by Azorero and Alonso (1998) that the solution for such Cauchy problem depends strongly on and the best constant λN,p in Hardy’s inequality, specifically, the local or global solutions for this problem depend on the different cases of 1 < p < 2, p ≥ 2 and λ > λN,p, λ < λN,p. By using the standard domain expansion technique and some convenient integrability conditions on the weighted function V(x), we first establish that the Cauchy problem has at least one global solution for every 1 < p < N. We then apply the theory of multivalued semigroups or multivalued semiflows to get L2 (ℝN) global attractor for the p-heat equation with 2 ≤ p < N. Furthermore, the global attractor also belongs to L2 (ℝN) ∩ Lα (ℝN) when is suitably large. ProQuest: ... denotes formulae omitted.]]></description><identifier>ISSN: 1468-1218</identifier><identifier>EISSN: 1878-5719</identifier><language>eng</language><publisher>Amsterdam: Elsevier BV</publisher><subject>Asymptotic methods ; Asymptotic properties ; Cauchy problems ; Integral calculus ; Non-Newtonian fluids ; Partial differential equations ; Quantum physics</subject><ispartof>Nonlinear analysis: real world applications, 2018-08, Vol.42, p.290</ispartof><rights>Copyright Elsevier BV Aug 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,778,782</link.rule.ids></links><search><creatorcontrib>Qian, Chenyin</creatorcontrib><creatorcontrib>Shen, Zifei</creatorcontrib><title>Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in R^sup N</title><title>Nonlinear analysis: real world applications</title><description><![CDATA[We consider asymptotic behavior for a parabolic equation (p-heat equation) with (sub-)critical Sobolev and Hardy exponent potential ... where 1 < p < N, (N ≥ 2). If V(x) ≡ λ and s = q = p, it is shown by Azorero and Alonso (1998) that the solution for such Cauchy problem depends strongly on and the best constant λN,p in Hardy’s inequality, specifically, the local or global solutions for this problem depend on the different cases of 1 < p < 2, p ≥ 2 and λ > λN,p, λ < λN,p. By using the standard domain expansion technique and some convenient integrability conditions on the weighted function V(x), we first establish that the Cauchy problem has at least one global solution for every 1 < p < N. We then apply the theory of multivalued semigroups or multivalued semiflows to get L2 (ℝN) global attractor for the p-heat equation with 2 ≤ p < N. Furthermore, the global attractor also belongs to L2 (ℝN) ∩ Lα (ℝN) when is suitably large. ProQuest: ... denotes formulae omitted.]]></description><subject>Asymptotic methods</subject><subject>Asymptotic properties</subject><subject>Cauchy problems</subject><subject>Integral calculus</subject><subject>Non-Newtonian fluids</subject><subject>Partial differential equations</subject><subject>Quantum physics</subject><issn>1468-1218</issn><issn>1878-5719</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNqNjs1KA0EQhAcxYPx5hwbPCztJdGfPEsnJg3o2dCa9yYRhejPdoxFf3lF8AE9VUF8VdWam1nWuuetsf1794t41dmbdhbkUObSt7ezcTs3X8hREKXkCHmAXeYMRhGPRwEkA0xZQNaNXzgIDZ9A9wYgZNxyDBzoW_EHhI-gefA4afF144RrT-29_hXn7CXQaOVFSCAme36SM8HRtJgNGoZs_vTK3j8vXh1UzZj4WEl0fuORUo_WsrXfbvneL-f-obwhPUH0</recordid><startdate>20180801</startdate><enddate>20180801</enddate><creator>Qian, Chenyin</creator><creator>Shen, Zifei</creator><general>Elsevier BV</general><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20180801</creationdate><title>Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in R^sup N</title><author>Qian, Chenyin ; Shen, Zifei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20713099843</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic methods</topic><topic>Asymptotic properties</topic><topic>Cauchy problems</topic><topic>Integral calculus</topic><topic>Non-Newtonian fluids</topic><topic>Partial differential equations</topic><topic>Quantum physics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qian, Chenyin</creatorcontrib><creatorcontrib>Shen, Zifei</creatorcontrib><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Nonlinear analysis: real world applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qian, Chenyin</au><au>Shen, Zifei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in R^sup N</atitle><jtitle>Nonlinear analysis: real world applications</jtitle><date>2018-08-01</date><risdate>2018</risdate><volume>42</volume><spage>290</spage><pages>290-</pages><issn>1468-1218</issn><eissn>1878-5719</eissn><abstract><![CDATA[We consider asymptotic behavior for a parabolic equation (p-heat equation) with (sub-)critical Sobolev and Hardy exponent potential ... where 1 < p < N, (N ≥ 2). If V(x) ≡ λ and s = q = p, it is shown by Azorero and Alonso (1998) that the solution for such Cauchy problem depends strongly on and the best constant λN,p in Hardy’s inequality, specifically, the local or global solutions for this problem depend on the different cases of 1 < p < 2, p ≥ 2 and λ > λN,p, λ < λN,p. By using the standard domain expansion technique and some convenient integrability conditions on the weighted function V(x), we first establish that the Cauchy problem has at least one global solution for every 1 < p < N. We then apply the theory of multivalued semigroups or multivalued semiflows to get L2 (ℝN) global attractor for the p-heat equation with 2 ≤ p < N. Furthermore, the global attractor also belongs to L2 (ℝN) ∩ Lα (ℝN) when is suitably large. ProQuest: ... denotes formulae omitted.]]></abstract><cop>Amsterdam</cop><pub>Elsevier BV</pub></addata></record> |
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| ispartof | Nonlinear analysis: real world applications, 2018-08, Vol.42, p.290 |
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| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Asymptotic methods Asymptotic properties Cauchy problems Integral calculus Non-Newtonian fluids Partial differential equations Quantum physics |
| title | Existence of global solutions and attractors for the parabolic equation with critical Sobolev and Hardy exponent in R^sup N |
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