On the geometry of the domain of the solution of nonlinear Cauchy problem
We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study also a variant of the inverse problem of the Cauchy problem...
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| creator | Figula, Ágota Menteshashvili, M. Z |
| description | We consider the Cauchy problem for a second order quasi-linear partial
differential equation with an admissible parabolic degeneration such that the
given functions described the initial conditions are defined on a closed
interval. We study also a variant of the inverse problem of the Cauchy problem
and prove that the considered inverse problem has a solution under certain
regularity condition. We illustrate the Cauchy and the inverse problems in some
interesting examples such that the families of the characteristic curves have
either common envelopes or singular points. In these cases the definition
domain of the solution of the differential equation contains a gap. |
| doi_str_mv | 10.48550/arxiv.1507.00166 |
| format | Article |
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differential equation with an admissible parabolic degeneration such that the
given functions described the initial conditions are defined on a closed
interval. We study also a variant of the inverse problem of the Cauchy problem
and prove that the considered inverse problem has a solution under certain
regularity condition. We illustrate the Cauchy and the inverse problems in some
interesting examples such that the families of the characteristic curves have
either common envelopes or singular points. In these cases the definition
domain of the solution of the differential equation contains a gap.</description><identifier>DOI: 10.48550/arxiv.1507.00166</identifier><language>eng</language><subject>Mathematics - Differential Geometry</subject><creationdate>2015-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1507.00166$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1507.00166$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Figula, Ágota</creatorcontrib><creatorcontrib>Menteshashvili, M. Z</creatorcontrib><title>On the geometry of the domain of the solution of nonlinear Cauchy problem</title><description>We consider the Cauchy problem for a second order quasi-linear partial
differential equation with an admissible parabolic degeneration such that the
given functions described the initial conditions are defined on a closed
interval. We study also a variant of the inverse problem of the Cauchy problem
and prove that the considered inverse problem has a solution under certain
regularity condition. We illustrate the Cauchy and the inverse problems in some
interesting examples such that the families of the characteristic curves have
either common envelopes or singular points. In these cases the definition
domain of the solution of the differential equation contains a gap.</description><subject>Mathematics - Differential Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNo1z71qwzAYhWEtHUrSC-hU3YDdz5L1SRqD6U8gkCW7kfXTCGwpKE6p777UbafDsxx4CXlsoG6VEPBsylf8rBsBsgZoEO_J_pjofPb0w-fJz2WhOax2eTIx_euax9sc8-qU0xiTN4V25mbPC72UPIx-2pK7YMarf_jbDTm9vpy69-pwfNt3u0NlUGIlgg6oGxYgKN6i4KiYFQNXAEEriUExyZzUqNXQStY6p7kdvHJgOUOr-YY8_d6uLf2lxMmUpf9p6tcm_g1tzEXR</recordid><startdate>20150701</startdate><enddate>20150701</enddate><creator>Figula, Ágota</creator><creator>Menteshashvili, M. Z</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20150701</creationdate><title>On the geometry of the domain of the solution of nonlinear Cauchy problem</title><author>Figula, Ágota ; Menteshashvili, M. Z</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-5f9f6912f0f834653682c5b3800f9876f8272d79698b4724dd93cbe8d0c326c93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Mathematics - Differential Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Figula, Ágota</creatorcontrib><creatorcontrib>Menteshashvili, M. Z</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Figula, Ágota</au><au>Menteshashvili, M. Z</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the geometry of the domain of the solution of nonlinear Cauchy problem</atitle><date>2015-07-01</date><risdate>2015</risdate><abstract>We consider the Cauchy problem for a second order quasi-linear partial
differential equation with an admissible parabolic degeneration such that the
given functions described the initial conditions are defined on a closed
interval. We study also a variant of the inverse problem of the Cauchy problem
and prove that the considered inverse problem has a solution under certain
regularity condition. We illustrate the Cauchy and the inverse problems in some
interesting examples such that the families of the characteristic curves have
either common envelopes or singular points. In these cases the definition
domain of the solution of the differential equation contains a gap.</abstract><doi>10.48550/arxiv.1507.00166</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Differential Geometry |
| title | On the geometry of the domain of the solution of nonlinear Cauchy problem |
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