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Asymptotic Behavior of Solutions to a Population Equation
SIAM Journal on Applied Mathematics, 1975This is a study of the large time behavior of solutions $x( t )$ to the nonlinear equation $x( t ) = \gamma \int_{t - 1}^t {x( \eta )} ( {1 - x( \eta )} )d\eta $ which satisfy $0\leqq x( t )\leqq 1$. It is known that such solutions approach constants as $t \to \infty $. This paper investigates the way in which the limit is attained. For $0\leqq \gamma \
Greenberg, J. M., Hoppensteadt, F.
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Asymptotic behavior of solutions: An application to stochastic NLP
Mathematical Programming, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arnab Sur, John R. Birge
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On the Asymptotic Behavior of Solutions of a Singular Cauchy Problem
Ukrainian Mathematical Journal, 2001The authors consider the singular Cauchy problem \[ \alpha (t) x'=F(t,x,x'), \qquad x(0)=0, \] with \(x:(0,\tau)\to\mathbb{R},\) \(\lim_{t\to {0+}} \alpha(t) = 0, \) \(\lim_{\alpha\to{0+}}\frac{\alpha(t)}{t}= \infty.\) First, the existence of a continuously differentiable solution \(x(t)\) such that \(x'(t)\to 0,\) \(t\to 0,\) is investigated.
Zernov, A. E., Meleshko, T. V.
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On the Asymptotic Behavior of Solutions to Kinetic Equations
SIAM Journal on Mathematical Analysis, 1985A “kinetic equation” here refers to a Cauchy initial value problem in $L^2 (( - \infty ,\infty ))$\[\frac{{dx_t }}{{dt}} = - Ax_t ,\qquad x_0 = g,\] where A is a bounded, symmetric, positive semidefinite, linear operator in $L^2 (( - \infty ,\infty ))$ with a mean-value property: $\smallint Ax = 0$.
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Asymptotic Behavior of Solutions for the Chafee-Infante Equation
Acta Mathematica Scientia, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Haochuan, Huang, Rui
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Asymptotic behavior of solutions of fuzzy differential equations
Fuzzy Sets and Systems, 1997Applying the Radstrom embedding theorem, the authors introduce first the machinery of the theory of regular fuzzy sets in a reflexive Banach space. Next, it is proved a few theorems on the asymptotic behavior of solutions to the fuzzy differential equation \(d\varphi/ds= F(s,\varphi(s))\), \(\varphi(0)= 0\).
Jong Yeoul Park +2 more
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Asymptotic Behavior of Optimal Solutions in Stochastic Programming
Mathematics of Operations Research, 1993Asymptotic behavior of optimal solutions x̂n of a sequence of stochastic programming problems is studied. Variational and generalized equations approaches are discussed. An expansion of x̂n in terms of a parametrized mathematical programming problem, depending on a single random vector, is given.
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The Asymptotic Behavior for Numerical Solution of a Volterra Equation
Acta Mathematicae Applicatae Sinica, English Series, 2003The author studies the long-time asymptotic stability and convergence properties for the numerical solution of a Volterra equation of parabolic type. The methods discussed are based on the first-second order backward difference methods. A discretization of the spatial partial differential operators by the finite element method is considered in their ...
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On the Asymptotic Behavior of Solutions of Semilinear Parabolic Equations
SIAM Journal on Applied Mathematics, 1975Let u be a solution of a second order semilinear parabolic equation which satisfies either Dirichlet or mixed boundary conditions. Let v be a stationary solution of this problem. Then by substituting $u = v + \varepsilon w$, and omitting terms of higher order in $\varepsilon $ than $O( \varepsilon )$, we may formally derive a linear problem.
Ewer, J. P. G., Peletier, L. A.
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Asymptotic Behavior of Solutions in Finite Difference Schemes
Bulletin of the Russian Academy of Sciences: Physics, 2018In many problems of numerically solving the Schrodinger equation, it is necessary to choose asymptotic distances that are many times greater than the characteristic size of the region of interaction. If the solutions to one-dimensional equations can be immediately chosen in a form that preserves unitarity, the preservation of probability (in, e.g., the
P. M. Krassovitskiy, F. M. Pen’kov
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