LEADER 04105nam 22006135 450 001 9910299762003321 005 20251116135203.0 010 $a3-319-19761-4 024 7 $a10.1007/978-3-319-19761-6 035 $a(CKB)3710000000444447 035 $a(EBL)3567557 035 $a(SSID)ssj0001534674 035 $a(PQKBManifestationID)11824404 035 $a(PQKBTitleCode)TC0001534674 035 $a(PQKBWorkID)11495003 035 $a(PQKB)10696449 035 $a(DE-He213)978-3-319-19761-6 035 $a(MiAaPQ)EBC3567557 035 $a(PPN)187686491 035 $a(EXLCZ)993710000000444447 100 $a20150708d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElliptic?hyperbolic partial differential equations $ea mini-course in geometric and quasilinear methods /$fby Thomas H. Otway 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (134 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 08$a3-319-19760-6 320 $aIncludes bibliographical references. 327 $aIntroduction -- Overview of elliptic?hyperbolic PDE -- Hodograph and partial hodograph methods -- Boundary value problems -- Bšacklund transformations and Hodge-theoretic methods -- Natural focusing. 330 $aThis text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example:   ? The heating of fusion plasmas by electromagnetic waves ? The behaviour of light near a caustic ? Extremal surfaces in the space of special relativity ? The formation of rapids; transonic and multiphase fluid flow ? The dynamics of certain models for elastic structures ? The shape of industrial surfaces such as windshields and airfoils ? Pathologies of traffic flow ? Harmonic fields in extended projective space   They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications.   Elliptic?Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aDifferential equations, Partial 606 $aMathematical physics 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 615 0$aDifferential equations, Partial. 615 0$aMathematical physics. 615 14$aPartial Differential Equations. 615 24$aMathematical Applications in the Physical Sciences. 676 $a515.353 700 $aOtway$b Thomas H.$4aut$4http://id.loc.gov/vocabulary/relators/aut$0167751 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299762003321 996 $aElliptic?hyperbolic partial differential equations$91522692 997 $aUNINA