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2000 Mathematics Subject Classification: Primary: 34B40; secondary: 35Q51, 35Q53By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator. As an illustration of...
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize the shallow water problem in height-flow rate formulation used to solve the flow in lakes and perfectly well-mixed sea. We establish a convergence result for the time-discretized problem when the momentum equation and the continuity equation are solved with the Galerkin method, without adding a penalization term in the continuity equation as it is made in...
We analyze the compressible isentropic Navier–Stokes equations (Lions, 1998) in the two-dimensional case with . These equations also modelize
the shallow water problem in height-flow rate formulation used to
solve the flow in lakes and perfectly well-mixed sea. We establish
a convergence result for the time-discretized problem when the
momentum equation and the continuity equation are solved with the
Galerkin method, without adding a penalization term in the
continuity equation as it is made in Lions...
It is proved in [1],[2] that in odd dimensional spaces any uniform decay
of the local energy implies that it must decay exponentially. We
extend this to even dimensional spaces and to more general perturbations
(including the transmission problem) showing that any uniform decay of the
local energy implies that it must decay like O(t^(−2n) ), t ≫ 1 being the time
and n being the space dimension.
A nonlocal model of phase separation in multicomponent systems is presented. It is derived from conservation principles and minimization of free energy containing a nonlocal part due to particle interaction. In contrast to the classical Cahn-Hilliard theory with higher order terms this leads to an evolution system of second order parabolic equations for the particle densities, coupled by nonlinear and nonlocal drift terms, and state equations which involve both chemical and interaction potential...
Given an open set of , bounded or unbounded, and a function with but allowed to change sign, we give a short proof...
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