LEADER 02983nam 22005895 450 001 9910751393603321 005 20251009083516.0 010 $a3-031-35550-4 024 7 $a10.1007/978-3-031-35550-9 035 $a(CKB)28487680100041 035 $a(MiAaPQ)EBC30782894 035 $a(Au-PeEL)EBL30782894 035 $a(DE-He213)978-3-031-35550-9 035 $a(PPN)272914606 035 $a(MiAaPQ)EBC30781992 035 $a(Au-PeEL)EBL30781992 035 $a(EXLCZ)9928487680100041 100 $a20231010d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInterfaces: Modeling, Analysis, Numerics /$fby Eberhard Bänsch, Klaus Deckelnick, Harald Garcke, Paola Pozzi 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2023. 215 $a1 online resource (186 pages) 225 1 $aOberwolfach Seminars,$x2296-5041 ;$v51 311 08$a9783031355493 327 $a1. Introduction -- 2. Some Notions from Differential Geometry -- 3. Modeling -- 4. Parametric Approaches for Geometric Evolution Equations and Interfaces -- 5. Implicit Approaches for Interfaces -- 6. Numerical Methods for Complex Interface Evolutions -- 7. Exercises. 330 $aThese lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization. We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions. 410 0$aOberwolfach Seminars,$x2296-5041 ;$v51 606 $aGeometry, Differential 606 $aDifferential equations 606 $aDifferential Geometry 606 $aDifferential Equations 615 0$aGeometry, Differential. 615 0$aDifferential equations. 615 14$aDifferential Geometry. 615 24$aDifferential Equations. 676 $a516.36 700 $aBa?nsch$b Eberhard$0434179 701 $aDeckelnick$b Klaus$01432904 701 $aGarcke$b Harald$0767190 701 $aPozzi$b Paola$0298291 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910751393603321 996 $aInterfaces: Modeling, Analysis, Numerics$93577976 997 $aUNINA