LEADER 02758nam 2200589 a 450 001 9910483749203321 005 20200520144314.0 010 $a3-642-18231-3 024 7 $a10.1007/978-3-642-18231-0 035 $a(CKB)2670000000076212 035 $a(SSID)ssj0000506050 035 $a(PQKBManifestationID)11313189 035 $a(PQKBTitleCode)TC0000506050 035 $a(PQKBWorkID)10529420 035 $a(PQKB)10391601 035 $a(DE-He213)978-3-642-18231-0 035 $a(MiAaPQ)EBC3066490 035 $a(PPN)151591326 035 $a(EXLCZ)992670000000076212 100 $a20110215d2011 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aRandom perturbation of PDEs and fluid dynamic models /$fFranco Flandoli 205 $a1st ed. 2011. 210 $aNew York $cSpringer$d2011 215 $a1 online resource (X, 182 p. 10 illus.) 225 1 $aLecture notes in mathematics. Ecole d'Ete de Probabilites de Saint-Flour XL-- 2010,$x0075-8434 ;$v2015 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-18230-5 320 $aIncludes bibliographical references. 327 $a1. Introduction to Uniqueness and Blow-up -- 2. Regularization by Additive Noise -- 3. Dyadic Models -- 4. Transport Equation -- 5. Other Models. Uniqueness and Singularities. 330 $aThis volume deals with the random perturbation of PDEs which lack well-posedness, mainly because of their non-uniqueness, in some cases because of blow-up. The aim is to show that noise may restore uniqueness or prevent blow-up. This is not a general or easy-to-apply rule, and the theory presented in the book is in fact a series of examples with a few unifying ideas. The role of additive and bilinear multiplicative noise is described and a variety of examples are included, from abstract parabolic evolution equations with non-Lipschitz nonlinearities to particular fluid dynamic models, like the dyadic model, linear transport equations and motion of point vortices. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2015. 606 $aPerturbation (Mathematics) 606 $aFluid dynamic measurements 606 $aDifferential equations, Partial 615 0$aPerturbation (Mathematics) 615 0$aFluid dynamic measurements. 615 0$aDifferential equations, Partial. 676 $a515.392 686 $a60H15$a60H10$a60J65$a35R60$a35Q35$a35B44$a76B03$2msc 700 $aFlandoli$b Franco$0314270 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483749203321 996 $aRandom perturbation of PDEs and fluid dynamic models$9261810 997 $aUNINA