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Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case | | Arnaud Debussche
; Martina Hofmanová
; Julien Vovelle
; | | Date: |
23 Sep 2013 | | Abstract: | 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 $L^1$-contraction
property. In comparison to the first-order case (Debussche and Vovelle, 2010)
and to the semilinear degenerate parabolic case (Hofmanov’a, 2013), the
present result contains two new ingredients: a generalized It^o 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. | | Source: | arXiv, 1309.5817 | | Services: | Forum | Review | PDF | Favorites | |
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