Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities
This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p...
Gespeichert in:
| Veröffentlicht in: | Acta mathematica Sinica. English series 2012-09, Vol.28 (9), p.1917-1936 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1936 |
|---|---|
| container_issue | 9 |
| container_start_page | 1917 |
| container_title | Acta mathematica Sinica. English series |
| container_volume | 28 |
| creator | Gan, Zai Hui Guo, Bo Ling Guo, Chun Xiao |
| description | This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study. |
| doi_str_mv | 10.1007/s10114-012-9238-8 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1136367795</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cqvip_id>43281439</cqvip_id><sourcerecordid>2730827501</sourcerecordid><originalsourceid>FETCH-LOGICAL-c375t-5be1463c75553041bf04ed201c16f7d9a4d3c3ef0200ec3bc66f011abe462723</originalsourceid><addsrcrecordid>eNp1kcFu3CAQhq0qlZqkfYDeqHLJxS0DBuxjs0rTSlEbKXvqBWF2vCb1wgbsrtynL9tdRVGkHhBo-P4ZxFcU74F-BErVpwQUoCopsLJhvC7rV8UpVLwplQR1cjzXAuSb4iylB0qFaKg8LearIeycX5NpS0JH7sMwjS74RMZAxh7Jwky2n8ldDO2AG9KF-K98gx6jGdwfXJGf5ldvYvhN7uc0Zmbnxp4swqZ1Pt_ehR3GcjlvkXwPfsg1E93oML0tXndmSPjuuJ8Xyy_Xy8XX8vbHzbfF59vSciXGUrQIleRWCSE4raDtaIUrRsGC7NSqMdWKW44dZZSi5a2VsstfYVqsJFOMnxeXh7bbGB4nTKPeuGRxGIzHMCUNwCWXSjUioxcv0IcwRZ8fp4FyJnleMlNwoGwMKUXs9Da6jYlzhvTehT640NmF3rvQdc6wQyZl1q8xPu_8_9CH46A--PVjzj1Nqjir90b5X0GKl7M</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1032633266</pqid></control><display><type>article</type><title>Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities</title><source>Springer Nature - Complete Springer Journals</source><source>Alma/SFX Local Collection</source><creator>Gan, Zai Hui ; Guo, Bo Ling ; Guo, Chun Xiao</creator><creatorcontrib>Gan, Zai Hui ; Guo, Bo Ling ; Guo, Chun Xiao</creatorcontrib><description>This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.</description><identifier>ISSN: 1439-8516</identifier><identifier>EISSN: 1439-7617</identifier><identifier>DOI: 10.1007/s10114-012-9238-8</identifier><language>eng</language><publisher>Heidelberg: Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</publisher><subject>Blowing ; Cauchy problem ; Cauchy problems ; Cauchy问题 ; Computational mathematics ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Nonlinearity ; Studies ; System theory ; Zakharov系统 ; 功率型 ; 广义 ; 有限时间 ; 爆破解 ; 负能量 ; 非线性</subject><ispartof>Acta mathematica Sinica. English series, 2012-09, Vol.28 (9), p.1917-1936</ispartof><rights>Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2012</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c375t-5be1463c75553041bf04ed201c16f7d9a4d3c3ef0200ec3bc66f011abe462723</citedby><cites>FETCH-LOGICAL-c375t-5be1463c75553041bf04ed201c16f7d9a4d3c3ef0200ec3bc66f011abe462723</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/85800X/85800X.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10114-012-9238-8$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10114-012-9238-8$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Gan, Zai Hui</creatorcontrib><creatorcontrib>Guo, Bo Ling</creatorcontrib><creatorcontrib>Guo, Chun Xiao</creatorcontrib><title>Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities</title><title>Acta mathematica Sinica. English series</title><addtitle>Acta. Math. Sin.-English Ser</addtitle><addtitle>Acta Mathematica Sinica</addtitle><description>This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.</description><subject>Blowing</subject><subject>Cauchy problem</subject><subject>Cauchy problems</subject><subject>Cauchy问题</subject><subject>Computational mathematics</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinearity</subject><subject>Studies</subject><subject>System theory</subject><subject>Zakharov系统</subject><subject>功率型</subject><subject>广义</subject><subject>有限时间</subject><subject>爆破解</subject><subject>负能量</subject><subject>非线性</subject><issn>1439-8516</issn><issn>1439-7617</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kcFu3CAQhq0qlZqkfYDeqHLJxS0DBuxjs0rTSlEbKXvqBWF2vCb1wgbsrtynL9tdRVGkHhBo-P4ZxFcU74F-BErVpwQUoCopsLJhvC7rV8UpVLwplQR1cjzXAuSb4iylB0qFaKg8LearIeycX5NpS0JH7sMwjS74RMZAxh7Jwky2n8ldDO2AG9KF-K98gx6jGdwfXJGf5ldvYvhN7uc0Zmbnxp4swqZ1Pt_ehR3GcjlvkXwPfsg1E93oML0tXndmSPjuuJ8Xyy_Xy8XX8vbHzbfF59vSciXGUrQIleRWCSE4raDtaIUrRsGC7NSqMdWKW44dZZSi5a2VsstfYVqsJFOMnxeXh7bbGB4nTKPeuGRxGIzHMCUNwCWXSjUioxcv0IcwRZ8fp4FyJnleMlNwoGwMKUXs9Da6jYlzhvTehT640NmF3rvQdc6wQyZl1q8xPu_8_9CH46A--PVjzj1Nqjir90b5X0GKl7M</recordid><startdate>20120901</startdate><enddate>20120901</enddate><creator>Gan, Zai Hui</creator><creator>Guo, Bo Ling</creator><creator>Guo, Chun Xiao</creator><general>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20120901</creationdate><title>Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities</title><author>Gan, Zai Hui ; Guo, Bo Ling ; Guo, Chun Xiao</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c375t-5be1463c75553041bf04ed201c16f7d9a4d3c3ef0200ec3bc66f011abe462723</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Blowing</topic><topic>Cauchy problem</topic><topic>Cauchy problems</topic><topic>Cauchy问题</topic><topic>Computational mathematics</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinearity</topic><topic>Studies</topic><topic>System theory</topic><topic>Zakharov系统</topic><topic>功率型</topic><topic>广义</topic><topic>有限时间</topic><topic>爆破解</topic><topic>负能量</topic><topic>非线性</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gan, Zai Hui</creatorcontrib><creatorcontrib>Guo, Bo Ling</creatorcontrib><creatorcontrib>Guo, Chun Xiao</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Acta mathematica Sinica. English series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gan, Zai Hui</au><au>Guo, Bo Ling</au><au>Guo, Chun Xiao</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities</atitle><jtitle>Acta mathematica Sinica. English series</jtitle><stitle>Acta. Math. Sin.-English Ser</stitle><addtitle>Acta Mathematica Sinica</addtitle><date>2012-09-01</date><risdate>2012</risdate><volume>28</volume><issue>9</issue><spage>1917</spage><epage>1936</epage><pages>1917-1936</pages><issn>1439-8516</issn><eissn>1439-7617</eissn><abstract>This paper deals with blowing up of solutions to the Cauchy problem for a class of general- ized Zakharov system with combined power-type nonlinearities in two and three space dimensions. On the one hand, for co = ＋oo we obtain two finite time blow-up results of solutions to the aforementioned 4 ≤ p 〈 N＋2/N-2 4 system. One is obtained under the condition a ≥ 0 and 1 ＋ 4/N or a 〈 0 and 1 〈 p 〈 1 ＋ （N = 2,3）; the other is established under the condition N = 3, 1 〈 p 〈 N=2/N-2 and α（p - 3） 〉 0. On the other hand, for co 〈 ＋∞ and α（p - 3） 〉 0, we prove a blow-up result for solutions with negative energy to the Zakharov system under study.</abstract><cop>Heidelberg</cop><pub>Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society</pub><doi>10.1007/s10114-012-9238-8</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1439-8516 |
| ispartof | Acta mathematica Sinica. English series, 2012-09, Vol.28 (9), p.1917-1936 |
| issn | 1439-8516 1439-7617 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1136367795 |
| source | Springer Nature - Complete Springer Journals; Alma/SFX Local Collection |
| subjects | Blowing Cauchy problem Cauchy problems Cauchy问题 Computational mathematics Mathematical analysis Mathematics Mathematics and Statistics Nonlinearity Studies System theory Zakharov系统 功率型 广义 有限时间 爆破解 负能量 非线性 |
| title | Blowing up of Solutions to the Cauchy Problem for the Generalized Zakharov System with Combined Power-Type Nonlinearities |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-01T19%3A58%3A24IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Blowing%20up%20of%20Solutions%20to%20the%20Cauchy%20Problem%20for%20the%20Generalized%20Zakharov%20System%20with%20Combined%20Power-Type%20Nonlinearities&rft.jtitle=Acta%20mathematica%20Sinica.%20English%20series&rft.au=Gan,%20Zai%20Hui&rft.date=2012-09-01&rft.volume=28&rft.issue=9&rft.spage=1917&rft.epage=1936&rft.pages=1917-1936&rft.issn=1439-8516&rft.eissn=1439-7617&rft_id=info:doi/10.1007/s10114-012-9238-8&rft_dat=%3Cproquest_cross%3E2730827501%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1032633266&rft_id=info:pmid/&rft_cqvip_id=43281439&rfr_iscdi=true |