Results 161 to 170 of about 13,185 (200)

Nonlinear singularly perturbed problems of ultra parabolic equations

Applied Mathematics and Mechanics, 2008
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Lin, Surong, Mo, Jiaqi
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Singularly perturbed boundary value problems

Acta Mathematicae Applicatae Sinica, 1999
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Some singular singularly-perturbed problems. II.

1999
Summary: This paper continuous part I published in the previous number of the same volume. For the corresponding summary see [ibid. 15, No. 3, 260--271 (1999; Zbl 0968.34015)].
Chang, K. W., Meng, J.
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Singularly Perturbed Boundary Value Problems

1991
Consider the two-point problem ey”+a(x)y’+b(x)y=f(x) on 0≤x≤1 where a(x)>0 and with the boundary values y(0) and y(1) prescribed. We shall suppose that a, b, and f are arbitrarily smooth, and we shall prove that the asymptotic solution will exist, be unique, and have the form $$y\left( {x,\varepsilon } \right) = Y\left( {x,\varepsilon } \right ...
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On Nonlinear Singularly Perturbed Initial Value Problems

SIAM Review, 1988
The author studies the singular perturbation initial value problem for the nonlinear system \(x'=f(x,y,t,\epsilon),\) \(\epsilon y'=g(x,y,t,\epsilon)\) on a bounded interval \([0,1]\) with smooth vector functions \(f\) and \(g\) of dimensions \(m\) and \(n\) respectively and with prescribed vector function \(x(0),y(0)\).
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Singularly perturbed initial value problems

1974
£y" + f(x,y,y',6) = O, 0 0 is a small parameter and "prime" denotes differentiation with respect to x. We shall formulate conditions under which the problem (i.i), (1.2) has a unique solution y(x, e) existing on the entire interval [0,b], for e sufficiently small. We shall also obtain explicit bounds on y(x,E) and y' (x,e) as g + 0. In particular, we
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Singularly Perturbed Optimal Control Problems. I: Convergence

SIAM Journal on Control and Optimization, 1976
The problem studied is as follows: when does the full solution of minimizing $x^0 (T)$, given \[\begin{gathered} \dot x(t) = f(x(t),y(t),u(t)),\quad u(t) \in U, \hfill \\ \varepsilon \dot y(t) = g(x(t),y(t),u(t)),\quad 0 \leqq t \leqq T, \hfill \\ \end{gathered} \] with boundary conditions on x and y, converge in some sense to the reduced solution of ...
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Singularly Perturbed Initial Value Problems

1991
Readers should refer to Murray (1977) and to earlier chemical engineering literature [especially Bowen et al. (1963) and Heinekin et al. (1967)] for experts’ explanations of the significance of the pseudo-steady-state hypothesis in biochemistry. The theory of Michaelis and Menton (1913) and Briggs and Haldane (1925) concerns a substrate S being ...
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Singularly perturbed problems with double singularity

Mathematical Notes, 1997
The author deals with systems of linear differential equations \[ \varepsilon^{m_1}\bigl(\delta_0(x)+\varepsilon\bigr)^{m_2}{dy\over dx}=A(x,\varepsilon)y+f(x), \] with \(\delta_0(x)>0\) for \(x\in(0,1)\), \(\delta_0 (0)=\delta_0(1)=0\), \(m_1,m_2\) are positive integers (which determine the two singularities \(x=0\) and \(x=1\), respectively) and the ...
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Stability of a singularly perturbed problem

Differential Equations, 2012
In this paper the author studies stability of the system of telegraph equations under perturbation of one boundary condition and in the presence of small regular perturbations. The investigation employs some ideas of A. N. Tikhonov which he introduced in the analysis of singularly perturbed systems.
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