Numerical verification for existence of a global-in-time solution to semilinear parabolic equations
This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semil...
Gespeichert in:
| Veröffentlicht in: | Journal of computational and applied mathematics 2017-05, Vol.315, p.1-16 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 16 |
|---|---|
| container_issue | |
| container_start_page | 1 |
| container_title | Journal of computational and applied mathematics |
| container_volume | 315 |
| creator | Mizuguchi, Makoto Takayasu, Akitoshi Kubo, Takayuki Oishi, Shin'ichi |
| description | This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t=t′≥0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t∈(0,τ],τ>0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given. |
| doi_str_mv | 10.1016/j.cam.2016.10.024 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1879992680</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0377042716305131</els_id><sourcerecordid>1879992680</sourcerecordid><originalsourceid>FETCH-LOGICAL-c439t-a05061304d2ee0033de7fa93fb9cb009b826660548c7ce6145cd4e592b364bde3</originalsourceid><addsrcrecordid>eNp9kEtPwzAQhC0EEuXxA7j5yCVlnThOLE6o4iVVcIGz5Tgb5MqJWzup4N_jtJw57exqZqT9CLlhsGTAxN1maXS_zJNM-xJyfkIWrK5kxqqqPiULKKoqA55X5-Qixg0ACMn4gpi3qcdgjXZ0n2aX1Gj9QDsfKH7bOOJgkPqOavrlfKNdZodstD3S6N10sI6eRuytswPqQLc66MY7ayjupkNXvCJnnXYRr__mJfl8evxYvWTr9-fX1cM6M7yQY6ahBMEK4G2OCFAULVadlkXXSNMAyKbOhRBQ8tpUBgXjpWk5ljJvCsGbFotLcnvs3Qa_mzCOqrfRoHN6QD9FNfOQMhc1JCs7Wk3wMQbs1DbYXocfxUDNQNVGJaBqBjqfEtCUuT9mMP2wtxhUNHbG09qAZlStt_-kfwH2Un9Y</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1879992680</pqid></control><display><type>article</type><title>Numerical verification for existence of a global-in-time solution to semilinear parabolic equations</title><source>Elsevier ScienceDirect Journals</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Mizuguchi, Makoto ; Takayasu, Akitoshi ; Kubo, Takayuki ; Oishi, Shin'ichi</creator><creatorcontrib>Mizuguchi, Makoto ; Takayasu, Akitoshi ; Kubo, Takayuki ; Oishi, Shin'ichi</creatorcontrib><description>This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t=t′≥0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t∈(0,τ],τ>0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/j.cam.2016.10.024</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Applications of mathematics ; Computation ; Existence theorems ; Global-in-time solution ; Mathematical analysis ; Mathematical models ; Semilinear parabolic equations ; Theorem proving ; Theorems ; Verified numerical computations</subject><ispartof>Journal of computational and applied mathematics, 2017-05, Vol.315, p.1-16</ispartof><rights>2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c439t-a05061304d2ee0033de7fa93fb9cb009b826660548c7ce6145cd4e592b364bde3</citedby><cites>FETCH-LOGICAL-c439t-a05061304d2ee0033de7fa93fb9cb009b826660548c7ce6145cd4e592b364bde3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0377042716305131$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Mizuguchi, Makoto</creatorcontrib><creatorcontrib>Takayasu, Akitoshi</creatorcontrib><creatorcontrib>Kubo, Takayuki</creatorcontrib><creatorcontrib>Oishi, Shin'ichi</creatorcontrib><title>Numerical verification for existence of a global-in-time solution to semilinear parabolic equations</title><title>Journal of computational and applied mathematics</title><description>This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t=t′≥0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t∈(0,τ],τ>0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given.</description><subject>Applications of mathematics</subject><subject>Computation</subject><subject>Existence theorems</subject><subject>Global-in-time solution</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Semilinear parabolic equations</subject><subject>Theorem proving</subject><subject>Theorems</subject><subject>Verified numerical computations</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kEtPwzAQhC0EEuXxA7j5yCVlnThOLE6o4iVVcIGz5Tgb5MqJWzup4N_jtJw57exqZqT9CLlhsGTAxN1maXS_zJNM-xJyfkIWrK5kxqqqPiULKKoqA55X5-Qixg0ACMn4gpi3qcdgjXZ0n2aX1Gj9QDsfKH7bOOJgkPqOavrlfKNdZodstD3S6N10sI6eRuytswPqQLc66MY7ayjupkNXvCJnnXYRr__mJfl8evxYvWTr9-fX1cM6M7yQY6ahBMEK4G2OCFAULVadlkXXSNMAyKbOhRBQ8tpUBgXjpWk5ljJvCsGbFotLcnvs3Qa_mzCOqrfRoHN6QD9FNfOQMhc1JCs7Wk3wMQbs1DbYXocfxUDNQNVGJaBqBjqfEtCUuT9mMP2wtxhUNHbG09qAZlStt_-kfwH2Un9Y</recordid><startdate>20170501</startdate><enddate>20170501</enddate><creator>Mizuguchi, Makoto</creator><creator>Takayasu, Akitoshi</creator><creator>Kubo, Takayuki</creator><creator>Oishi, Shin'ichi</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><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>20170501</creationdate><title>Numerical verification for existence of a global-in-time solution to semilinear parabolic equations</title><author>Mizuguchi, Makoto ; Takayasu, Akitoshi ; Kubo, Takayuki ; Oishi, Shin'ichi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c439t-a05061304d2ee0033de7fa93fb9cb009b826660548c7ce6145cd4e592b364bde3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applications of mathematics</topic><topic>Computation</topic><topic>Existence theorems</topic><topic>Global-in-time solution</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Semilinear parabolic equations</topic><topic>Theorem proving</topic><topic>Theorems</topic><topic>Verified numerical computations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mizuguchi, Makoto</creatorcontrib><creatorcontrib>Takayasu, Akitoshi</creatorcontrib><creatorcontrib>Kubo, Takayuki</creatorcontrib><creatorcontrib>Oishi, Shin'ichi</creatorcontrib><collection>CrossRef</collection><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>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mizuguchi, Makoto</au><au>Takayasu, Akitoshi</au><au>Kubo, Takayuki</au><au>Oishi, Shin'ichi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical verification for existence of a global-in-time solution to semilinear parabolic equations</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>2017-05-01</date><risdate>2017</risdate><volume>315</volume><spage>1</spage><epage>16</epage><pages>1-16</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><abstract>This paper presents a method of numerical verification for the existence of a global-in-time solution to a class of semilinear parabolic equations. Such a method is based on two main theorems in this paper. One theorem gives a sufficient condition for proving the existence of a solution to the semilinear parabolic equations with the initial point t=t′≥0. If the sufficient condition does not hold, the other theorem is used for enclosing the solution for time t∈(0,τ],τ>0 in a neighborhood of a numerical solution. Numerical results of obtaining a global-in-time solution for a certain semilinear parabolic equation are also given.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cam.2016.10.024</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 2017-05, Vol.315, p.1-16 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1879992680 |
| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| subjects | Applications of mathematics Computation Existence theorems Global-in-time solution Mathematical analysis Mathematical models Semilinear parabolic equations Theorem proving Theorems Verified numerical computations |
| title | Numerical verification for existence of a global-in-time solution to semilinear parabolic equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-23T19%3A23%3A13IST&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=Numerical%20verification%20for%20existence%20of%20a%20global-in-time%20solution%20to%20semilinear%20parabolic%20equations&rft.jtitle=Journal%20of%20computational%20and%20applied%20mathematics&rft.au=Mizuguchi,%20Makoto&rft.date=2017-05-01&rft.volume=315&rft.spage=1&rft.epage=16&rft.pages=1-16&rft.issn=0377-0427&rft.eissn=1879-1778&rft_id=info:doi/10.1016/j.cam.2016.10.024&rft_dat=%3Cproquest_cross%3E1879992680%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=1879992680&rft_id=info:pmid/&rft_els_id=S0377042716305131&rfr_iscdi=true |