Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip
An inhomogeneous Tricomi equation is considered in a strip with a polynomial right-hand side. It is shown that the Dirichlet boundary value problem with polynomial boundary conditions has a polynomial solution. An algorithm for constructing this polynomial solution is given and examples are consider...
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| creator | Algazin, Oleg D |
| description | An inhomogeneous Tricomi equation is considered in a strip with a polynomial
right-hand side. It is shown that the Dirichlet boundary value problem with
polynomial boundary conditions has a polynomial solution. An algorithm for
constructing this polynomial solution is given and examples are considered. If
the strip lies in the ellipticity region of the equation, then this solution is
unique in the class of functions of polynomial growth. If the strip lies in a
mixed region, then the solution of the Dirichlet problem is not unique in the
class of functions of polynomial growth, but it is unique in the class of
polynomials. |
| doi_str_mv | 10.48550/arxiv.1807.04627 |
| format | Article |
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right-hand side. It is shown that the Dirichlet boundary value problem with
polynomial boundary conditions has a polynomial solution. An algorithm for
constructing this polynomial solution is given and examples are considered. If
the strip lies in the ellipticity region of the equation, then this solution is
unique in the class of functions of polynomial growth. If the strip lies in a
mixed region, then the solution of the Dirichlet problem is not unique in the
class of functions of polynomial growth, but it is unique in the class of
polynomials.</description><identifier>DOI: 10.48550/arxiv.1807.04627</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs ; Mathematics - Mathematical Physics ; Physics - Mathematical Physics</subject><creationdate>2018-07</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>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1807.04627$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1807.04627$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Algazin, Oleg D</creatorcontrib><title>Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip</title><description>An inhomogeneous Tricomi equation is considered in a strip with a polynomial
right-hand side. It is shown that the Dirichlet boundary value problem with
polynomial boundary conditions has a polynomial solution. An algorithm for
constructing this polynomial solution is given and examples are considered. If
the strip lies in the ellipticity region of the equation, then this solution is
unique in the class of functions of polynomial growth. If the strip lies in a
mixed region, then the solution of the Dirichlet problem is not unique in the
class of functions of polynomial growth, but it is unique in the class of
polynomials.</description><subject>Mathematics - Analysis of PDEs</subject><subject>Mathematics - Mathematical Physics</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tOwzAUBb1hgQofwAr_QILjd5dVeUqVCqL76Nr1VS05cXBSRP-eNrA6i9EcaQi5a1gtrVLsAcpP_K4by0zNpObmmny853Tqcxch0TGn4xRzP9KMdDoE-hhL9IcUJjqU7FLoKOYyk90ZnCUavo5wUWjsKdBxKnG4IVcIaQy3_7sgn89Pu_Vrtdm-vK1Xmwq0MRUylFLIBrX0innFjbeopLF7jcYIcFw4w5cKlAjWKesQ0VktQHmn-F4syP3f65zUDiV2UE7tJa2d08QvmDdKIg</recordid><startdate>20180708</startdate><enddate>20180708</enddate><creator>Algazin, Oleg D</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20180708</creationdate><title>Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip</title><author>Algazin, Oleg D</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-f0f44341f64c50c527c8f5478d6f773ab23b7295a53e8b58bfffb863a5cb52d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Mathematics - Analysis of PDEs</topic><topic>Mathematics - Mathematical Physics</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Algazin, Oleg D</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Algazin, Oleg D</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip</atitle><date>2018-07-08</date><risdate>2018</risdate><abstract>An inhomogeneous Tricomi equation is considered in a strip with a polynomial
right-hand side. It is shown that the Dirichlet boundary value problem with
polynomial boundary conditions has a polynomial solution. An algorithm for
constructing this polynomial solution is given and examples are considered. If
the strip lies in the ellipticity region of the equation, then this solution is
unique in the class of functions of polynomial growth. If the strip lies in a
mixed region, then the solution of the Dirichlet problem is not unique in the
class of functions of polynomial growth, but it is unique in the class of
polynomials.</abstract><doi>10.48550/arxiv.1807.04627</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs Mathematics - Mathematical Physics Physics - Mathematical Physics |
| title | Polynomial solutions of the Dirichlet problem for the Tricomi equation in a strip |
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