5,559 research outputs found
The determination of asymptotic and periodic behavior of dynamic systems arising in control system analysis Final report
Asymptotic and periodic behavior prediction for nonlinear control system with mathematical model of rigid body vehicl
Eliminating flutter for clamped von Karman plates immersed in subsonic flows
We address the long-time behavior of a non-rotational von Karman plate in an
inviscid potential flow. The model arises in aeroelasticity and models the
interaction between a thin, nonlinear panel and a flow of gas in which it is
immersed [6, 21, 23]. Recent results in [16, 18] show that the plate component
of the dynamics (in the presence of a physical plate nonlinearity) converge to
a global compact attracting set of finite dimension; these results were
obtained in the absence of mechanical damping of any type. Here we show that,
by incorporating mechanical damping the full flow-plate system, full
trajectories---both plate and flow---converge strongly to (the set of)
stationary states. Weak convergence results require "minimal" interior damping,
and strong convergence of the dynamics are shown with sufficiently large
damping. We require the existence of a "good" energy balance equation, which is
only available when the flows are subsonic. Our proof is based on first showing
the convergence properties for regular solutions, which in turn requires
propagation of initial regularity on the infinite horizon. Then, we utilize the
exponential decay of the difference of two plate trajectories to show that full
flow-plate trajectories are uniform-in-time Hadamard continuous. This allows us
to pass convergence properties of smooth initial data to finite energy type
initial data. Physically, our results imply that flutter (a non-static end
behavior) does not occur in subsonic dynamics. While such results were known
for rotational (compact/regular) plate dynamics [14] (and references therein),
the result presented herein is the first such result obtained for
non-regularized---the most physically relevant---models
Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
We are interested in the strong convergence and almost sure stability of
Euler-Maruyama (EM) type approximations to the solutions of stochastic
differential equations (SDEs) with non-linear and non-Lipschitzian
coefficients. Motivation comes from finance and biology where many widely
applied models do not satisfy the standard assumptions required for the strong
convergence. In addition we examine the globally almost surely asymptotic
stability in this non-linear setting for EM type schemes. In particular, we
present a stochastic counterpart of the discrete LaSalle principle from which
we deduce stability properties for numerical methods
Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations
We present a method to solve initial-boundary value problems for linear and
integrable nonlinear differential-difference evolution equations. The method is
the discrete version of the one developed by A. S. Fokas to solve
initial-boundary value problems for linear and integrable nonlinear partial
differential equations via an extension of the inverse scattering transform.
The method takes advantage of the Lax pair formulation for both linear and
nonlinear equations, and is based on the simultaneous spectral analysis of both
parts of the Lax pair. A key role is also played by the global algebraic
relation that couples all known and unknown boundary values. Even though
additional technical complications arise in discrete problems compared to
continuum ones, we show that a similar approach can also solve initial-boundary
value problems for linear and integrable nonlinear differential-difference
equations. We demonstrate the method by solving initial-boundary value problems
for the discrete analogue of both the linear and the nonlinear Schrodinger
equations, comparing the solution to those of the corresponding continuum
problems. In the linear case we also explicitly discuss Robin-type boundary
conditions not solvable by Fourier series. In the nonlinear case we also
identify the linearizable boundary conditions, we discuss the elimination of
the unknown boundary datum, we obtain explicitly the linear and continuum limit
of the solution, and we write down the soliton solutions.Comment: 41 pages, 3 figures, to appear in Inverse Problem
Asymptotic behavior and existence of solutions for singular elliptic equations
We study the asymptotic behavior, as tends to infinity, of solutions
for the homogeneous Dirichlet problem associated to singular semilinear
elliptic equations whose model is where is an open, bounded subset of \RN and is a
bounded function. We deal with the existence of a limit equation under two
different assumptions on : either strictly positive on every compactly
contained subset of or only nonnegative. Through this study we deduce
optimal existence results of positive solutions for the homogeneous Dirichlet
problem associated to Comment: 31 page
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