Results 151 to 160 of about 13,060 (202)

Nonsmooth regular perturbations of singularly perturbed problems

Journal of Differential Equations, 2023
In this paper, a boundary value problem for singularly and regularly perturbed quasilinear ordinary differential equations (ODEs) in divergence form is considered. More precisely, the problem under consideration is \[ \begin{aligned} -\varepsilon^2(a(x,u(x), \varepsilon)u'(x))'+b(x,u(x),\varepsilon)&=\delta g(x), \qquad x\in(-1,1),\\ u(-1)&=u'(1)=0 ...
Nikolai N. Nefedov, Andrey O. Orlov, Lutz Recke, Klaus R. Schneider   +3 more
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Singularly Perturbed Eigenvalue Problems

SIAM Journal on Applied Mathematics, 1987
This paper is concerned with eigenvalue problems of singularly perturbed linear ordinary differential equations. A common way to treat such problems is to derive an approximating eigenvalue problem by the use of matched asymptotic expansions. It is shown that under appropriate assumptions a domain in the complex plane can be identified, in which the ...
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Singularly Perturbed Semilinear Robin Problems

Studies in Applied Mathematics, 1982
Several phenomena of current interest in catalytic reaction theory can be phrased in terms of solutions of singularly perturbed, second‐order, semilinear differential equations satisfying boundary conditions of Robin type. This paper offers a mathematical theory for such problems in both the scalar and the vector case, and treats some examples ...
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Quasilinear singularly perturbed problem with boundary perturbation

Journal of Zhejiang University-SCIENCE A, 2004
A 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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Interior Estimates for Singularly Perturbed Problems

Zeitschrift für Analysis und ihre Anwendungen, 1984
The 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, 1999
Summary: 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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Singularly Perturbed Optimal Tracking Problem

Differential Equations
We 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, 1989
The 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, Nefedov, N. N., O'Malley, Robert E. jun.   +2 more
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Singularly Perturbed Cauchy Problems and Contrast Structures

Differential Equations, 2002
The 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

2021
This 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, Lanza de Cristoforis, Massimo, Musolino, Paolo   +2 more
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