Stochastic non-isotropic degenerate parabolic–hyperbolic equations

Well-posedness for Non-isotropic Degenerate Parabolic-hyperbolic Equations

We develop a well-posedness theory for solutions in L to the Cauchy problem of general degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity. A new notion of entropy and kinetic solutions and a corresponding kinetic formulation are developed which extends the hyperbolic case. The notion of kinetic solutions applies to more general situations than that of entropy solutions; a...

Singular-Degenerate Multivalued Stochastic Fast Diffusion Equations

We consider singular-degenerate, multivalued stochastic fast diffusion equations with multiplicative Lipschitz continuous noise. In particular, this includes the stochastic sign fast diffusion equation arising from the BakTang-Wiesenfeld model for self-organized criticality. A well-posedness framework based on stochastic variational inequalities (SVI) is developed, characterizing solutions to t...

Degenerate Stochastic Differential Equations, Flows and Hypoellipticity

A Class of Degenerate Stochastic Differential Equations with Non-lipschitz Coefficients

We obtain sufficient condition for SDEs to evolve in the positive orthrant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.

Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Abstract. In this article, using DiPerna-Lions theory [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinea...