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Nonlinear parabolic equations for measures. (English) Zbl 1286.35137
St. Petersbg. Math. J. 25, No. 1, 43-62 (2014); translation from Algebra Anal. 25, No. 1, 64-93 (2013).
Summary: A new existence result is established for weak parabolic equations for probability measures. Sufficient conditions are given for the existence of local and global-in-time probability solutions of the Cauchy problem for such equations. Some conditions under which global-in-time solutions do not exist are indicated.

MSC:
35K59 Quasilinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35R60 PDEs with randomness, stochastic partial differential equations
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