LEADER 03720nam 22006375 450 001 9910136471503321 005 20200702092434.0 010 $a3-319-41069-5 024 7 $a10.1007/978-3-319-41069-2 035 $a(CKB)3710000000873058 035 $a(DE-He213)978-3-319-41069-2 035 $a(MiAaPQ)EBC6302380 035 $a(MiAaPQ)EBC5596353 035 $a(Au-PeEL)EBL5596353 035 $a(OCoLC)959954316 035 $a(PPN)195510593 035 $a(EXLCZ)993710000000873058 100 $a20160930d2016 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Porous Media Equations /$fby Viorel Barbu, Giuseppe Da Prato, Michael Röckner 205 $a1st ed. 2016. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016. 215 $a1 online resource (IX, 202 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2163 311 $a3-319-41068-7 320 $aIncludes bibliographical references and index. 327 $aForeword -- Preface -- Introduction -- Equations with Lipschitz nonlinearities -- Equations with maximal monotone nonlinearities -- Variational approach to stochastic porous media equations -- L1-based approach to existence theory for stochastic porous media equations -- The stochastic porous media equations in Rd -- Transition semigroups and ergodicity of invariant measures -- Kolmogorov equations -- A Two analytical inequalities -- Bibliography -- Glossary -- Translator?s note -- Index. 330 $aFocusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2163 606 $aProbabilities 606 $aPartial differential equations 606 $aFluids 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 $aFluid- and Aerodynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/P21026 615 0$aProbabilities. 615 0$aPartial differential equations. 615 0$aFluids. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aFluid- and Aerodynamics. 676 $a519.2 700 $aBarbu$b Viorel$4aut$4http://id.loc.gov/vocabulary/relators/aut$013745 702 $aDa Prato$b Giuseppe$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aRöckner$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910136471503321 996 $aStochastic Porous Media Equations$92196292 997 $aUNINA