On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes
We study the Cauchy problem for a degenerate parabolic equation with source and inhomogeneous density of the form in the case where the initial function slowly vanishes as | x | → ∞: We establish conditions for the existence and nonexistence of a global (in time) solution. These conditions strongly...
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| Veröffentlicht in: | Ukrainian mathematical journal 2013-04, Vol.64 (11), p.1698-1715 |
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| container_end_page | 1715 |
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| container_issue | 11 |
| container_start_page | 1698 |
| container_title | Ukrainian mathematical journal |
| container_volume | 64 |
| creator | Martynenko, A. V. Tedeev, A. F. Shramenko, V. N. |
| description | We study the Cauchy problem for a degenerate parabolic equation with source and inhomogeneous density of the form
in the case where the initial function slowly vanishes as |
x
| → ∞: We establish conditions for the existence and nonexistence of a global (in time) solution. These conditions strongly depend on the behavior of the initial data as |
x
| → ∞: In the case of global solvability, we establish a sharp estimate of the solution for large times. |
| doi_str_mv | 10.1007/s11253-013-0745-2 |
| format | Article |
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in the case where the initial function slowly vanishes as |
x
| → ∞: We establish conditions for the existence and nonexistence of a global (in time) solution. These conditions strongly depend on the behavior of the initial data as |
x
| → ∞: In the case of global solvability, we establish a sharp estimate of the solution for large times.</description><identifier>ISSN: 0041-5995</identifier><identifier>EISSN: 1573-9376</identifier><identifier>DOI: 10.1007/s11253-013-0745-2</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Mathematics ; Mathematics and Statistics ; Statistics</subject><ispartof>Ukrainian mathematical journal, 2013-04, Vol.64 (11), p.1698-1715</ispartof><rights>Springer Science+Business Media New York 2013</rights><rights>COPYRIGHT 2013 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c327t-370d04db3ab7cfe32ea4dd735b89ef836e53540178c288b3c31ae77bd6c0c7b03</citedby><cites>FETCH-LOGICAL-c327t-370d04db3ab7cfe32ea4dd735b89ef836e53540178c288b3c31ae77bd6c0c7b03</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11253-013-0745-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11253-013-0745-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Martynenko, A. V.</creatorcontrib><creatorcontrib>Tedeev, A. F.</creatorcontrib><creatorcontrib>Shramenko, V. N.</creatorcontrib><title>On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes</title><title>Ukrainian mathematical journal</title><addtitle>Ukr Math J</addtitle><description>We study the Cauchy problem for a degenerate parabolic equation with source and inhomogeneous density of the form
in the case where the initial function slowly vanishes as |
x
| → ∞: We establish conditions for the existence and nonexistence of a global (in time) solution. These conditions strongly depend on the behavior of the initial data as |
x
| → ∞: In the case of global solvability, we establish a sharp estimate of the solution for large times.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Statistics</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kc9u3CAQxlGVSN38eYDceAGnYIzxHqNVm0aKlEtyRgMe1kRe2IKd1T5K3zY47rlCCA0zv2808xFyx9k9Z0z9yJzXUlSMl6saWdXfyIZLJaqtUO0F2TDW8Eput_I7ucr5nbFCdWpD_r4EOg1IDQ7w4WOi0dEcx3nyMeQlWJI7mO1wpscUzYgH6koZ0B73GDDBhPQICUwcvaX4Z4YFpSc_DUVoThapX1tYyEhPAyb8Cn3wk4eRujnYLySP8TSe6QcEnwfMN-TSwZjx9t97Td5-_Xzd_a6eXx6fdg_PlRW1miqhWM-a3ggwyjoUNULT90pI023RdaJFKWTDuOps3XVGWMEBlTJ9a5lVholrcr_q7mFE7YOLUwJbTo8Hb2NA58v_gxCyrVvF6wLwFbAp5pzQ6WPyB0hnzZlezNCrGbqYoRcz9MLUK5NLbdhj0u9lN6HM9R_oE8fWj_4</recordid><startdate>20130401</startdate><enddate>20130401</enddate><creator>Martynenko, A. V.</creator><creator>Tedeev, A. F.</creator><creator>Shramenko, V. N.</creator><general>Springer US</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20130401</creationdate><title>On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes</title><author>Martynenko, A. V. ; Tedeev, A. F. ; Shramenko, V. N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c327t-370d04db3ab7cfe32ea4dd735b89ef836e53540178c288b3c31ae77bd6c0c7b03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Martynenko, A. V.</creatorcontrib><creatorcontrib>Tedeev, A. F.</creatorcontrib><creatorcontrib>Shramenko, V. N.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Martynenko, A. V.</au><au>Tedeev, A. F.</au><au>Shramenko, V. N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2013-04-01</date><risdate>2013</risdate><volume>64</volume><issue>11</issue><spage>1698</spage><epage>1715</epage><pages>1698-1715</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>We study the Cauchy problem for a degenerate parabolic equation with source and inhomogeneous density of the form
in the case where the initial function slowly vanishes as |
x
| → ∞: We establish conditions for the existence and nonexistence of a global (in time) solution. These conditions strongly depend on the behavior of the initial data as |
x
| → ∞: In the case of global solvability, we establish a sharp estimate of the solution for large times.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s11253-013-0745-2</doi><tpages>18</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2013-04, Vol.64 (11), p.1698-1715 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A335626712 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Statistics |
| title | On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes |
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