LEADER 04459nam 22006975 450 001 9910299976003321 005 20200706224436.0 010 $a3-319-08287-6 024 7 $a10.1007/978-3-319-08287-5 035 $a(CKB)3710000000281306 035 $a(EBL)1967921 035 $a(OCoLC)895661026 035 $a(SSID)ssj0001386399 035 $a(PQKBManifestationID)11860975 035 $a(PQKBTitleCode)TC0001386399 035 $a(PQKBWorkID)11349407 035 $a(PQKB)11737670 035 $a(MiAaPQ)EBC1967921 035 $a(DE-He213)978-3-319-08287-5 035 $a(PPN)183096886 035 $a(EXLCZ)993710000000281306 100 $a20141114d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aClassical and Stochastic Laplacian Growth$b[electronic resource] /$fby Björn Gustafsson, Razvan Teodorescu, Alexander Vasil?ev 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (329 p.) 225 1 $aAdvances in Mathematical Fluid Mechanics,$x2297-0320 300 $aDescription based upon print version of record. 311 $a3-319-08286-8 320 $aIncludes bibliographical references and index. 327 $a1 Introduction and Background -- 2 Rational and Other Explicit Strong Solutions -- 3 Weak Solutions and Related Topics -- 4 Geometric Properties -- 5 Capacities and Isoperimetric Inequalities -- 6 Laplacian Growth and Random Matrix Theory -- 7 Integrability and Moments -- 8 Shape Evolution and Integrability -- 9 Stochastic Löwner and Löwner-Kufarev Evolution -- References -- List of Symbols -- Index. 330 $aThis monograph covers a multitude of concepts, results, and research topics originating from a classical moving-boundary problem in two dimensions (idealized Hele-Shaw flows, or classical Laplacian growth), which has strong connections to many exciting modern developments in mathematics and theoretical physics. Of particular interest are the relations between Laplacian growth and the infinite-size limit of ensembles of random matrices with complex eigenvalues; integrable hierarchies of differential equations and their spectral curves; classical and stochastic Löwner evolution and critical phenomena in two-dimensional statistical models; weak solutions of hyperbolic partial differential equations of singular-perturbation type; and resolution of singularities for compact Riemann surfaces with anti-holomorphic involution. The book also provides an abundance of exact classical solutions, many explicit examples of dynamics by conformal mapping as well as a solid foundation of potential theory. An extensive bibliography covering over twelve decades of results and an introduction rich in historical and biographical details complement the eight main chapters of this monograph. Given its systematic and consistent notation and background results, this book provides a self-contained resource. It is accessible to a wide readership, from beginner graduate students to researchers from various fields in natural sciences and mathematics. 410 0$aAdvances in Mathematical Fluid Mechanics,$x2297-0320 606 $aMathematical physics 606 $aNumerical analysis 606 $aFunctions of complex variables 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 615 0$aMathematical physics. 615 0$aNumerical analysis. 615 0$aFunctions of complex variables. 615 14$aMathematical Physics. 615 24$aNumerical Analysis. 615 24$aFunctions of a Complex Variable. 676 $a516 700 $aGustafsson$b Björn$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721273 702 $aTeodorescu$b Razvan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aVasil?ev$b Alexander$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299976003321 996 $aClassical and Stochastic Laplacian Growth$92535767 997 $aUNINA