返回Google圖書搜尋

Degenerate Parabolic Stochastic Partial Differential Equations

Arnaud DebusscheMartina HofmanováJulien Vovelle

其他書名	Quasilinear Case
出版	Niedersächsische Staats- und Universitätsbibliothek, 2013
URL	http://books.google.com.hk/books?id=8rvxvgEACAAJ&hl=&source=gbs_api

註釋In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic solution and develop a well-posedness theory that includes also an L1-contraction property. In comparison to the previous works of the authors concerning stochastic hyperbolic conservation laws (Debussche and Vovelle, 2010) and semilinear degenerate parabolic SPDEs (Hofmanová, 2013), the present result contains two new ingredients that provide simpler and more effective method of the proof: a generalized Itô formula that permits a rigorous derivation of the kinetic formulation even in the case of weak solutions of certain nondegenerate approximations and a direct proof of strong convergence of these approximations to the desired kinetic solution of the degenerate problem.