Results 161 to 170 of about 91,926 (215)

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 ...
openaire   +1 more source

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 ...
openaire   +2 more sources

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.
openaire   +1 more source

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.
openaire   +2 more sources

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.
openaire   +1 more source

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
openaire   +2 more sources

Square Powers of Singularly Perturbed Operators

Mathematische Nachrichten, 1995
AbstractWe use the method of self‐adjoint extensions to define a self‐adjoint operator AT as the singular perturbation of a given self‐adjoint operator A by a singular operator T on a Hilbert space.We also find the structure of a singular operator Q such that the singular perturbation of A2 by Q satisfies (A2)Q = (AT)2. We obtain the explicit form of Q
Albeverio, Sergio, Karwowski, Witold, Koshmanenko, Vladimir   +2 more
openaire   +2 more sources

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
openaire   +1 more source

Discretization of the semilinear singularly perturbed problem

Nonlinear Analysis: Theory, Methods & Applications, 1997
The 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
openaire   +1 more source

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.
openaire   +2 more sources