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Approximation theory in the context of probability density function turns out to go beyond the classical idea of orthogonal projection. Special tools have to be designed so as to respect the nonnegativity of the approximate function. We develop here and justify from the theoretical point of view an approximation procedure introduced by Levermore [Levermore, J. Stat. Phys. 83 (1996) 1021–1065] and based on an entropy minimization principle under moment constraints. We prove in particular a global...
Approximation theory in the context of probability density
function turns out to go beyond the classical idea of orthogonal
projection. Special tools have to be designed so as to respect the
nonnegativity of the approximate function. We develop here and
justify from the theoretical point of view an approximation
procedure introduced by Levermore [Levermore, J. Stat. Phys.83 (1996) 1021–1065] and based on an
entropy minimization principle under moment constraints. We prove
in particular...
We prove existence of weak solutions to doubly degenerate diffusion equations
by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains with Dirichlet or Neumann boundary conditions. The function can be an inhomogeneity or a nonlinearity involving terms of the form or . In the appendix, an introduction to weak differentiability...
Inertial manifold with delay (IMD) for dissipative systems of second order in time is
constructed. This result is applied to the study of different asymptotic properties of
solutions. Using IMD, we construct approximate inertial manifolds containing all the
stationary solutions and give a new characterization of the K-invariant manifold.
The behavior of an ordinary differential equation for the low wave number velocity
mode is analyzed. This equation was derived in [5]
by an iterative process on the two-dimensional Navier-Stokes equations (NSE). It
resembles the NSE in form, except
that the kinematic viscosity is replaced by an iterated viscosity
which is a partial sum, dependent on the low-mode velocity. The convergence of
this sum as the number of iterations is taken to be arbitrarily large is explored.
This leads to a limiting...
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