Functional separable solutions of nonlinear convection–diffusion equations with variable coefficients
•Nonlinear convection-diffusion equations are considered.•Arbitrary functions are included in equations.•New functional separable solutions are presented.•Specific equations and their exact solutions are analyzed.•Solutions of delay convection-diffusion equations are given. The paper presents a numb...
Gespeichert in:
| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2019-07, Vol.73, p.379-390 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 390 |
|---|---|
| container_issue | |
| container_start_page | 379 |
| container_title | Communications in nonlinear science & numerical simulation |
| container_volume | 73 |
| creator | Polyanin, Andrei D. |
| description | •Nonlinear convection-diffusion equations are considered.•Arbitrary functions are included in equations.•New functional separable solutions are presented.•Specific equations and their exact solutions are analyzed.•Solutions of delay convection-diffusion equations are given.
The paper presents a number of new functional separable solutions to nonlinear convection–diffusion equations of the formc(x)ut=[a(x)ux]x+[b(x)+p(x)f(u)]ux,where f(u) is an arbitrary function. It shows that any three of the four variable coefficients a(x), b(x), c(x), p(x) of such equations can be chosen arbitrarily, and the remaining coefficient can be expressed through the others. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more-complex nonlinear PDEs with variable coefficients. Also some functional separable solutions to nonlinear convection–diffusion equations with delayut=uxx+a(x)f(u,w)ux,w=u(x,t−τ),where τ > 0 is the delay time and f(u, w) is an arbitrary function of two arguments, are obtained. |
| doi_str_mv | 10.1016/j.cnsns.2019.02.022 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2232032853</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S1007570419300553</els_id><sourcerecordid>2232032853</sourcerecordid><originalsourceid>FETCH-LOGICAL-c331t-210eacb948015e73538d1346f9333db4360fe31135a1c7dfc570f29bd28ef06d3</originalsourceid><addsrcrecordid>eNp9UM1KxDAYDKLguvoEXgqeW_PT34MHWVwVFrzoOaTJF02pyW7SrnjzHXxDn8R061kY-IaPmYEZhC4Jzggm5XWXSRtsyCgmTYZpBD1CC1JXdVrRKj-OHOMqLSqcn6KzEDocXU2RL9DrerRyMM6KPgmwFV60PSTB9eP0DInTiXW2NxaET6Szeziof76-ldF6DJEnsBvFrP4ww1uyF94cUqQDrY00YIdwjk606ANc_N0lelnfPa8e0s3T_ePqdpNKxsiQUoJByLbJa0wKqFjBakVYXuqGMabanJVYAyOEFYLISmkZK2natIrWoHGp2BJdzblb73YjhIF3bvSxXeCUMooZrQsWVWxWSe9C8KD51pt34T85wXxalHf8sCifFuWYRtDoupldEAvsDXgepnISlPFxFq6c-df_C4DCg2U</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2232032853</pqid></control><display><type>article</type><title>Functional separable solutions of nonlinear convection–diffusion equations with variable coefficients</title><source>Access via ScienceDirect (Elsevier)</source><creator>Polyanin, Andrei D.</creator><creatorcontrib>Polyanin, Andrei D.</creatorcontrib><description>•Nonlinear convection-diffusion equations are considered.•Arbitrary functions are included in equations.•New functional separable solutions are presented.•Specific equations and their exact solutions are analyzed.•Solutions of delay convection-diffusion equations are given.
The paper presents a number of new functional separable solutions to nonlinear convection–diffusion equations of the formc(x)ut=[a(x)ux]x+[b(x)+p(x)f(u)]ux,where f(u) is an arbitrary function. It shows that any three of the four variable coefficients a(x), b(x), c(x), p(x) of such equations can be chosen arbitrarily, and the remaining coefficient can be expressed through the others. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more-complex nonlinear PDEs with variable coefficients. Also some functional separable solutions to nonlinear convection–diffusion equations with delayut=uxx+a(x)f(u,w)ux,w=u(x,t−τ),where τ > 0 is the delay time and f(u, w) is an arbitrary function of two arguments, are obtained.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2019.02.022</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Boundary value problems ; Coefficients ; Convection-diffusion equation ; Convection–diffusion equations with delay ; Delay time ; Diffusion ; Equations with variable coefficients ; Exact solutions ; Functional separable solutions ; Linear equations ; Mathematical analysis ; Nonlinear convection–diffusion equations ; Nonlinear equations ; Nonlinear systems ; Partial differential equations</subject><ispartof>Communications in nonlinear science & numerical simulation, 2019-07, Vol.73, p.379-390</ispartof><rights>2019 Elsevier B.V.</rights><rights>Copyright Elsevier Science Ltd. Jul 15, 2019</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c331t-210eacb948015e73538d1346f9333db4360fe31135a1c7dfc570f29bd28ef06d3</citedby><cites>FETCH-LOGICAL-c331t-210eacb948015e73538d1346f9333db4360fe31135a1c7dfc570f29bd28ef06d3</cites><orcidid>0000-0002-2610-0590</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.cnsns.2019.02.022$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Polyanin, Andrei D.</creatorcontrib><title>Functional separable solutions of nonlinear convection–diffusion equations with variable coefficients</title><title>Communications in nonlinear science & numerical simulation</title><description>•Nonlinear convection-diffusion equations are considered.•Arbitrary functions are included in equations.•New functional separable solutions are presented.•Specific equations and their exact solutions are analyzed.•Solutions of delay convection-diffusion equations are given.
The paper presents a number of new functional separable solutions to nonlinear convection–diffusion equations of the formc(x)ut=[a(x)ux]x+[b(x)+p(x)f(u)]ux,where f(u) is an arbitrary function. It shows that any three of the four variable coefficients a(x), b(x), c(x), p(x) of such equations can be chosen arbitrarily, and the remaining coefficient can be expressed through the others. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more-complex nonlinear PDEs with variable coefficients. Also some functional separable solutions to nonlinear convection–diffusion equations with delayut=uxx+a(x)f(u,w)ux,w=u(x,t−τ),where τ > 0 is the delay time and f(u, w) is an arbitrary function of two arguments, are obtained.</description><subject>Boundary value problems</subject><subject>Coefficients</subject><subject>Convection-diffusion equation</subject><subject>Convection–diffusion equations with delay</subject><subject>Delay time</subject><subject>Diffusion</subject><subject>Equations with variable coefficients</subject><subject>Exact solutions</subject><subject>Functional separable solutions</subject><subject>Linear equations</subject><subject>Mathematical analysis</subject><subject>Nonlinear convection–diffusion equations</subject><subject>Nonlinear equations</subject><subject>Nonlinear systems</subject><subject>Partial differential equations</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9UM1KxDAYDKLguvoEXgqeW_PT34MHWVwVFrzoOaTJF02pyW7SrnjzHXxDn8R061kY-IaPmYEZhC4Jzggm5XWXSRtsyCgmTYZpBD1CC1JXdVrRKj-OHOMqLSqcn6KzEDocXU2RL9DrerRyMM6KPgmwFV60PSTB9eP0DInTiXW2NxaET6Szeziof76-ldF6DJEnsBvFrP4ww1uyF94cUqQDrY00YIdwjk606ANc_N0lelnfPa8e0s3T_ePqdpNKxsiQUoJByLbJa0wKqFjBakVYXuqGMabanJVYAyOEFYLISmkZK2natIrWoHGp2BJdzblb73YjhIF3bvSxXeCUMooZrQsWVWxWSe9C8KD51pt34T85wXxalHf8sCifFuWYRtDoupldEAvsDXgepnISlPFxFq6c-df_C4DCg2U</recordid><startdate>20190715</startdate><enddate>20190715</enddate><creator>Polyanin, Andrei D.</creator><general>Elsevier B.V</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-2610-0590</orcidid></search><sort><creationdate>20190715</creationdate><title>Functional separable solutions of nonlinear convection–diffusion equations with variable coefficients</title><author>Polyanin, Andrei D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c331t-210eacb948015e73538d1346f9333db4360fe31135a1c7dfc570f29bd28ef06d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Boundary value problems</topic><topic>Coefficients</topic><topic>Convection-diffusion equation</topic><topic>Convection–diffusion equations with delay</topic><topic>Delay time</topic><topic>Diffusion</topic><topic>Equations with variable coefficients</topic><topic>Exact solutions</topic><topic>Functional separable solutions</topic><topic>Linear equations</topic><topic>Mathematical analysis</topic><topic>Nonlinear convection–diffusion equations</topic><topic>Nonlinear equations</topic><topic>Nonlinear systems</topic><topic>Partial differential equations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Polyanin, Andrei D.</creatorcontrib><collection>CrossRef</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Polyanin, Andrei D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Functional separable solutions of nonlinear convection–diffusion equations with variable coefficients</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2019-07-15</date><risdate>2019</risdate><volume>73</volume><spage>379</spage><epage>390</epage><pages>379-390</pages><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>•Nonlinear convection-diffusion equations are considered.•Arbitrary functions are included in equations.•New functional separable solutions are presented.•Specific equations and their exact solutions are analyzed.•Solutions of delay convection-diffusion equations are given.
The paper presents a number of new functional separable solutions to nonlinear convection–diffusion equations of the formc(x)ut=[a(x)ux]x+[b(x)+p(x)f(u)]ux,where f(u) is an arbitrary function. It shows that any three of the four variable coefficients a(x), b(x), c(x), p(x) of such equations can be chosen arbitrarily, and the remaining coefficient can be expressed through the others. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more-complex nonlinear PDEs with variable coefficients. Also some functional separable solutions to nonlinear convection–diffusion equations with delayut=uxx+a(x)f(u,w)ux,w=u(x,t−τ),where τ > 0 is the delay time and f(u, w) is an arbitrary function of two arguments, are obtained.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2019.02.022</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0002-2610-0590</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1007-5704 |
| ispartof | Communications in nonlinear science & numerical simulation, 2019-07, Vol.73, p.379-390 |
| issn | 1007-5704 1878-7274 |
| language | eng |
| recordid | cdi_proquest_journals_2232032853 |
| source | Access via ScienceDirect (Elsevier) |
| subjects | Boundary value problems Coefficients Convection-diffusion equation Convection–diffusion equations with delay Delay time Diffusion Equations with variable coefficients Exact solutions Functional separable solutions Linear equations Mathematical analysis Nonlinear convection–diffusion equations Nonlinear equations Nonlinear systems Partial differential equations |
| title | Functional separable solutions of nonlinear convection–diffusion equations with variable coefficients |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T13%3A49%3A29IST&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=Functional%20separable%20solutions%20of%20nonlinear%20convection%E2%80%93diffusion%20equations%20with%20variable%20coefficients&rft.jtitle=Communications%20in%20nonlinear%20science%20&%20numerical%20simulation&rft.au=Polyanin,%20Andrei%20D.&rft.date=2019-07-15&rft.volume=73&rft.spage=379&rft.epage=390&rft.pages=379-390&rft.issn=1007-5704&rft.eissn=1878-7274&rft_id=info:doi/10.1016/j.cnsns.2019.02.022&rft_dat=%3Cproquest_cross%3E2232032853%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=2232032853&rft_id=info:pmid/&rft_els_id=S1007570419300553&rfr_iscdi=true |