Results 151 to 160 of about 19,649 (184)

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 Volterra Integral Equations

SIAM Journal on Applied Mathematics, 1987
The authors study the singularly perturbed Volterra integral equation \[ \epsilon u(t)=\int^{t}_{0}K(t-s)F(u(s),s) ds,\quad t\geq 0, \] where \(\epsilon\) is a small parameter, with the objective of developing a methodology that yields the appropriate ''inner'' and ''outer'' integral equations, each of which is defined on the whole domain of interest ...
Angell, J. S., Olmstead, W. E.
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Singularly Perturbed Evolution Inclusions

SIAM Journal on Control and Optimization, 2010
Consider the control system \[ \dot{x}(t)+ A_{1}x \in F(x,y,u(t)),\quad x(0) = x^{0}\in H_{1},\quad u(t)\in U, \tag{1} \] \[ \varepsilon\dot{y}(t)+ A_{2}y \in G(x,y,u(t)),\quad y(0) = y^{0}\in H_2,\quad t\in [0,1], \tag{2} \] where \(F:H_{1}\times H_{2}\times U \rightrightarrows H_{1}\), \(G:H_{1}\times H_{2}\times U \rightrightarrows H_{2}\) are ...
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Singularly Perturbed Semilinear Systems

Studies in Applied Mathematics, 1979
Solutions of a singularly perturbed vector boundary‐value problem are studied under the principal assumption that the trivial solution of the unperturbed equation is stable in certain senses. This is accomplished by constructing special invariant regions in which solutions display the kind of nonuniformity known as boundary‐layer behavior.
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Singularly perturbed fuzzy initial value problems

Expert Systems with Applications, 2023
In this work, we have firstly introduced singularly perturbed fuzzy initial value problems (SPFIVPs) and then we have given an algorithm for the solutions of them by using the extension principle given by Zadeh. We have presented some results on the behaviour of the α-cuts of the solutions.
Nurettin Doğan, Selami Bayeğ, Raziye Mert, Ömer Akın   +3 more
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Singularly Perturbed Systems

1984
In this chapter we turn our attention to some vector boundary value problems which may be regarded as vector analogs of the scalar problems. However, as the reader will see, our results for vector problems are very incomplete, especially in comparison with the scalar theory.
K. W. Chang, F. A. Howes
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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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Singularly perturbed Chern–Simons theory

Journal of Mathematical Physics, 1990
The Chern–Simons theory of an SU(2) gauge theory in three dimensions is looked at from a perturbative point of view. The pure Chern–Simons action is generalized by adding a conventional Yang–Mills action term. This acts as a singular perturbation. The resulting theory has a moduli space containing that of the pure Chern–Simons version; for certain ...
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Singularly perturbed pseudoparabolic equation

Mathematical Methods in the Applied Sciences, 2016
An asymptotic expansion of the contrasting structure‐like solution of the generalized Kolmogorov–Petrovskii–Piskunov equation is presented. A generalized maximum principle for the pseudoparabolic equations is developed. This, together with the generalized differential inequalities method, allows to prove the consistence and convergence of the ...
Bykov, Alexey, Panin, Alexander, Sharlo, Alena   +2 more
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Unfolding Singularly Perturbed Bogdanov Points

SIAM Journal on Mathematical Analysis, 2000
Summary: Bogdanov points that occur in the fast dynamics of singular perturbation problems are often encountered in applications; e.g., in the van der Pol-Duffing oscillator [\textit{M. Koper}, Physica D 80, No. 1-2, 72--94 (1995; Zbl 0889.34034)] or in the FitzHugh-Nagumo equation [\textit{W.-J. Beyn} and \textit{M. Stiefenhofer}, J. Dyn.
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