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81
Stochastic generalized porous media and fast diffusion equations
, 2005
"... We present a generalization of KrylovRozovskii’s result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for σfinite reference measures, where the drift te ..."
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Cited by 38 (17 self)
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We present a generalization of KrylovRozovskii’s result on the existence and uniqueness of solutions to monotone stochastic differential equations. As an application, the stochastic generalized porous media and fast diffusion equations are studied for σfinite reference measures, where the drift term is given by a negative definite operator acting on a timedependent function, which belongs to a large class of functions comparable with the socalled Nfunctions in the theory of Orlicz spaces. AMS subject Classification: 76S05, 60H15.
HARNACK INEQUALITY AND APPLICATIONS FOR STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS
 SUBMITTED TO THE ANNALS OF PROBABILITY
, 2006
"... By using coupling and Girsanov transformations, the dimensionfree Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As applications, explicit upper bounds of the Lpnorm of the density as ..."
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Cited by 37 (10 self)
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By using coupling and Girsanov transformations, the dimensionfree Harnack inequality and the strong Feller property are proved for transition semigroups of solutions to a class of stochastic generalized porous media equations. As applications, explicit upper bounds of the Lpnorm of the density as well as hypercontractivity, ultracontractivity and compactness of the corresponding semigroup are derived.
Harnack Inequality and Strong Feller Property for Stochastic FastDiffusion Equations
, 2007
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Existence and uniqueness of nonnegative solutions to the stochastic porous media equation
, 2007
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Strong Solutions of Stochastic Generalized Porous Media Equations: Existence, Uniqueness and Ergodicity
, 2008
"... Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal decay for the solution of the classical (deterministic) poro ..."
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Cited by 29 (11 self)
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Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal decay for the solution of the classical (deterministic) porous medium equation.
Finite Element Approximation Of Transport Of Reactive Solutes In Porous Media Part 1 Error Estimates For NonEquilibrium Adsorption Processes
, 1997
"... . In this paper we analyse a fully practical piecewise linear finite element approximation; involving numerical integration, backward Euler time discretization and possibly regularization; of the following degenerate parabolic system arising in a model of reactive solute transport in porous media: F ..."
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Cited by 24 (4 self)
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. In this paper we analyse a fully practical piecewise linear finite element approximation; involving numerical integration, backward Euler time discretization and possibly regularization; of the following degenerate parabolic system arising in a model of reactive solute transport in porous media: Find fu(x; t); v(x; t)g such that @ t u + @ t v \Gamma \Deltau = f in\Omega \Theta (0; T ] u = 0 on @\Omega \Theta (0; T ] @ t v = k('(u) \Gamma v) in\Omega \Theta (0; T ] u(\Delta ; 0) = g 1 (\Delta) v(\Delta ; 0) = g 2 (\Delta) in\Omega ae R d ; 1 d 3 for given data k 2 R + , f , g 1 , g 2 and a monotonically increasing ' 2 C 0 (R) " C 1 (\Gamma1; 0] [ (0; 1) satisfying '(0) = 0; which is only locally Holder continuous, with exponent p 2 (0; 1), at the origin; e.g. '(s) j [s] p + . This lack of Lipschitz continuity at the origin limits the regularity of the unique solution fu; vg and leads to difficulties in the finite element error analysis. Key words. finite elemen...
Large deviations for stochastic evolution equations with small multiplcative noise
"... The FreidlinWentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. Roughly speaking, besides the assumptions for existence and uniqueness of the solution, one only need assume some additio ..."
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Cited by 24 (10 self)
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The FreidlinWentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. Roughly speaking, besides the assumptions for existence and uniqueness of the solution, one only need assume some additional assumptions on diffusion coefficient in order to obtain Large deviation principle for the distribution of solution. As applications we can apply the main result to different type examples of SPDEs (e.g. stochastic reactiondiffusion equation, stochastic porous media and fast diffusion equations, stochastic pLaplacian equation) in Hilbert space. The weak convergence approach is employed to verify the Laplace principle, which is equivalent to large deviation principle in our framework. AMS subject Classification: 60F10, 60H15.
Selfsimilar solutions of a fast diffusion equation that do not conserve mass
, 1994
"... do not conserve mass ..."
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A hierarchy of models for typeII superconductors
 SIAM Rev
, 2000
"... A hierarchy of models for typeII superconductors is presented. Through appropriate asymptotic limits we pass from the mesoscopic GinzburgLandau model to the London model with isolated superconducting vortices as line singularities, to vortexdensity models, and finally to macroscopic criticalstat ..."
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Cited by 16 (2 self)
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A hierarchy of models for typeII superconductors is presented. Through appropriate asymptotic limits we pass from the mesoscopic GinzburgLandau model to the London model with isolated superconducting vortices as line singularities, to vortexdensity models, and finally to macroscopic criticalstate models.