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Quasilinear singularly perturbed problem with boundary perturbation
Journal of Zhejiang University-SCIENCE A, 2004A class of quasilinear singularly perturbed problems with boundary perturbation is considered. Under suitable conditions, using theory of differential inequalities we studied the asymptotic behavior of the solution for the boundary value problem.
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, 2020
Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems.
T. A. Bullo, G. Duressa, G. Degla
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Robust finite difference method is introduced in order to solve singularly perturbed two parametric parabolic convection-diffusion problems.
T. A. Bullo, G. Duressa, G. Degla
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Interior Estimates for Singularly Perturbed Problems
Zeitschrift für Analysis und ihre Anwendungen, 1984The solution of the Dirichlet problem for a singularly perturbed elliptic differential equation \epsilon L_1u + L_0u = h of order 2m converges, for
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Analytic Regularity for a Singularly Perturbed Problem
SIAM Journal on Mathematical Analysis, 1999Summary: A singularly perturbed equation of elliptic-elliptic type in two dimensions is considered. We assume analyticity of the input data, i.e., the boundary of the domain is an analytic curve, the boundary data are analytic, and the right-hand side is analytic.
Melenk, Jens Markus, Schwab, Christoph
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On adaptive mesh for the initial boundary value singularly perturbed delay Sobolev problems
Numerical Methods for Partial Differential Equations, 2019A uniform finite difference method on a B‐mesh is applied to solve the initial‐boundary value problem for singularly perturbed delay Sobolev equations. To solve the foresold problem, finite difference scheme on a special nonuniform mesh, whose solution ...
A. B. Chiyaneh, H. Duru
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Singularly Perturbed Optimal Tracking Problem
Differential EquationsWe consider a singularly perturbed optimal tracking problem with a given etalon trajectory in the case of incomplete information about the state vector in the presence of external disturbances. To analyze the differential equations that arise when solving this problem, the decomposition method is used, which is based on the technique of integral ...
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On Singular Singularly Perturbed Initial Value Problems
SIAM Journal on Applied Mathematics, 1989The singular system \(\epsilon z'(t)=F(z,t,\epsilon)\) with a small \(\epsilon >0\) and give z(0) is solved under certain assumptions in a finite interval [0,T] up to an O(\(\epsilon)\) in the case that F(Z,t,0) has an infinite family of solutions Z(t). The investigation combines the methods of \textit{A. B. Vasileva} and \textit{V. F.
Gu, Zhongmei +2 more
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Singularly Perturbed Cauchy Problems and Contrast Structures
Differential Equations, 2002The authors consider the Cauchy problem for a singularly perturbed system of second-order differential equations. Sufficient conditions for the appearance of contrast structures of step and spike types for systems with piecewise smooth right-hand side were obtained by the authors [Differ. Equ. 36, No. 11, 1493--1510 (2000; Zbl 1056.34520), ibid. 37, No.
Neimark, Yu. I., Smirnova, V. N.
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Singularly Perturbed Boundary Value Problems
2021This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions.
Dalla Riva, Matteo +2 more
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Discretization of the semilinear singularly perturbed problem
Nonlinear Analysis: Theory, Methods & Applications, 1997The authors discuss the construction of a spline function for a class of singularly perturbed singular problems: \[ -\varepsilon^2 x^{2\alpha} u'' (x) + b(x,u)=0, \quad x \in (0,1), \quad u(0)=u(1)=0 \tag{1} \] with parameter \(\alpha \in [0, 0.5) \) and a perturbation parameter \(\varepsilon \in (0, \varepsilon_0 ]\), \(\varepsilon_0 \ll 1\).
Uzelac, Zorica, Surla, Katarina
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