02902nam 22005415 450 99646650400331620240613225400.03-642-18231-310.1007/978-3-642-18231-0(CKB)2670000000076212(SSID)ssj0000506050(PQKBManifestationID)11313189(PQKBTitleCode)TC0000506050(PQKBWorkID)10529420(PQKB)10391601(DE-He213)978-3-642-18231-0(MiAaPQ)EBC3066490(PPN)151591326(EXLCZ)99267000000007621220110301d2011 u| 0engurnn#008mamaatxtccrRandom Perturbation of PDEs and Fluid Dynamic Models École d’Été de Probabilités de Saint-Flour XL – 2010 /by Franco Flandoli1st ed. 2011.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2011.1 online resource (X, 182 p. 10 illus.)École d'Été de Probabilités de Saint-Flour,0721-5363 ;2015Bibliographic Level Mode of Issuance: Monograph3-642-18230-5 Includes bibliographical references.1. Introduction to Uniqueness and Blow-up -- 2. Regularization by Additive Noise -- 3. Dyadic Models -- 4. Transport Equation -- 5. Other Models. Uniqueness and Singularities.This 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.Lecture notes in mathematics (Springer-Verlag).École d'été de probabilités de Saint-Flour0721-5363 ;2015ProbabilitiesProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Probabilities.Probability Theory and Stochastic Processes.515.39260H1560H1060J6535R6035Q3535B4476B03mscFlandoli Francoauthttp://id.loc.gov/vocabulary/relators/aut314270Flandoli FrancoBOOK996466504003316Random perturbation of PDEs and fluid dynamic models261810UNISA