LEADER 05084nam 22006975 450 001 9910300256903321 005 20200706084041.0 010 $a3-319-22354-2 024 7 $a10.1007/978-3-319-22354-4 035 $a(DE-He213)978-3-319-22354-4 035 $a(MiAaPQ)EBC6312883 035 $a(MiAaPQ)EBC5577113 035 $a(Au-PeEL)EBL5577113 035 $a(OCoLC)1066195799 035 $a(PPN)190532092 035 $a(CKB)3710000000521694 035 $a(EXLCZ)993710000000521694 100 $a20151006d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Partial Differential Equations: An Introduction /$fby Wei Liu, Michael Röckner 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (VI, 266 p.) 225 1 $aUniversitext,$x0172-5939 327 $aMotivation, Aims and Examples -- Stochastic Integral in Hilbert Spaces -- SDEs in Finite Dimensions -- SDEs in Infinite Dimensions and Applications to SPDEs -- SPDEs with Locally Monotone Coefficients -- Mild Solutions. 330 $aThis book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ?variational approach?, it also contains a short account on the ?semigroup (or mild solution) approach?. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee non-explosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the ?locally monotone case? is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the well-known case of globally monotone coefficients, substantially widens the applicability of the results. In addition, it leads to a unified approach and to simplified proofs in many classical examples. These include a large number of SPDEs not covered by the ?globally monotone case?, such as, for exa mple, stochastic Burgers or stochastic 2D and 3D Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic surface growth models. To keep the book self-contained and prerequisites low, necessary results about SDEs in finite dimensions are also included with complete proofs as well as a chapter on stochastic integration on Hilbert spaces. Further fundamentals (for example, a detailed account on the Yamada-Watanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a one-year graduate course. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aPartial differential equations 606 $aDifferential equations 606 $aMathematical physics 606 $aGame theory 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aGame Theory, Economics, Social and Behav. Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13011 615 0$aProbabilities. 615 0$aPartial differential equations. 615 0$aDifferential equations. 615 0$aMathematical physics. 615 0$aGame theory. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aOrdinary Differential Equations. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aGame Theory, Economics, Social and Behav. Sciences. 676 $a519.2 700 $aLiu$b Wei$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755646 702 $aRöckner$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300256903321 996 $aStochastic Partial Differential Equations: An Introduction$92541512 997 $aUNINA