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Mathematical methods in the applied sciences, 2018
In the present work, we consider a parabolic convection‐diffusion‐reaction problem where the diffusion and convection terms are multiplied by two small parameters, respectively.
M. Chandru, P. Das, H. Ramos
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In the present work, we consider a parabolic convection‐diffusion‐reaction problem where the diffusion and convection terms are multiplied by two small parameters, respectively.
M. Chandru, P. Das, H. Ramos
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Nonlinear singularly perturbed problems of ultra parabolic equations
Applied Mathematics and Mechanics, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lin, Surong, Mo, Jiaqi
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Concentrating solutions for singularly perturbed double phase problems with nonlocal reaction
Journal of Differential Equations, 2023Wen Zhang +2 more
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Singularly perturbed boundary value problems
Acta Mathematicae Applicatae Sinica, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Some singular singularly-perturbed problems. II.
1999Summary: 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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Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control
, 2013The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon.
V. Gaitsgory, Sergey Rossomakhine
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Singularly Perturbed Boundary Value Problems
1991Consider 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, 1988The 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, 1976The 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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