887 research outputs found
Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators
The aim of the present paper is to study the regularity properties of the
solution of a backward stochastic differential equation with a monotone
generator in infinite dimension. We show some applications to the nonlinear
Kolmogorov equation and to stochastic optimal control
Advectional enhancement of eddy diffusivity under parametric disorder
Frozen parametric disorder can lead to appearance of sets of localized
convective currents in an otherwise stable (quiescent) fluid layer heated from
below. These currents significantly influence the transport of an admixture (or
any other passive scalar) along the layer. When the molecular diffusivity of
the admixture is small in comparison to the thermal one, which is quite typical
in nature, disorder can enhance the effective (eddy) diffusivity by several
orders of magnitude in comparison to the molecular diffusivity. In this paper
we study the effect of an imposed longitudinal advection on delocalization of
convective currents, both numerically and analytically; and report subsequent
drastic boost of the effective diffusivity for weak advection.Comment: 14 pages, 6 figures, for Topical Issue of Physica Scripta "2nd Intl.
Conf. on Turbulent Mixing and Beyond
Well-posedness for a class of nonlinear degenerate parabolic equations
In this paper we obtain well-posedness for a class of semilinear weakly
degenerate reaction-diffusion systems with Robin boundary conditions. This
result is obtained through a Gagliardo-Nirenberg interpolation inequality and
some embedding results for weighted Sobolev spaces
Some homogenization and corrector results for nonlinear monotone operators
This paper deals with the limit behaviour of the solutions of quasi-linear
equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon
_h},Du_h\right)\right)=f_h on with Dirichlet boundary conditions.
The sequence tends to and the map is
periodic in , monotone in and satisfies suitable continuity
conditions. It is proved that weakly in , where is the solution of a homogenized problem \
-\limfunc{div}(b(x,Du))=f on . We also prove some corrector results,
i.e. we find such that in
Correctors for some nonlinear monotone operators
In this paper we study homogenization of quasi-linear partial differential
equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right)
\right) =f_h on with Dirichlet boundary conditions. Here the
sequence tends to as
and the map is periodic in monotone in
and satisfies suitable continuity conditions. We prove that
weakly in as where
is the solution of a homogenized problem of the form -\mbox{div}\left(
b\left( x,Du\right) \right) =f on We also derive an explicit
expression for the homogenized operator and prove some corrector results,
i.e. we find such that in
Interference phenomena in scalar transport induced by a noise finite correlation time
The role played on the scalar transport by a finite, not small, correlation
time, , for the noise velocity is investigated, both analytically and
numerically. For small 's a mechanism leading to enhancement of
transport has recently been identified and shown to be dominating for any type
of flow. For finite non-vanishing 's we recognize the existence of a
further mechanism associated with regions of anticorrelation of the Lagrangian
advecting velocity. Depending on the extension of the anticorrelated regions,
either an enhancement (corresponding to constructive interference) or a
depletion (corresponding to destructive interference) in the turbulent
transport now takes place.Comment: 8 pages, 3 figure
On weak convergence of locally periodic functions
We prove a generalization of the fact that periodic functions converge weakly
to the mean value as the oscillation increases. Some convergence questions
connected to locally periodic nonlinear boundary value problems are also
considered.Comment: arxiv version is already officia
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