Results 221 to 230 of about 8,505 (264)

SINGULAR PERTURBATIONS OF QUADRATIC MAPS

International Journal of Bifurcation and Chaos, 2004
We give a complete description of the dynamics of the mapping fε(z)=z2+(ε/z) for positive real values of ε. We then consider two generalizations: the case of complex ε and the mapping z→zn+(ε/zm), where ε is positive and real. In both cases we provide a full characterization of the map for a certain set of parameters, and give observations based on ...
Robert L. Devaney, Kresimir Josic, Yakov Shapiro   +2 more
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Singular Perturbation and the Energy of Folds

Journal of Nonlinear Science, 2000
The paper deals with the asymptotic behaviour as \(\varepsilon\downarrow 0\) of the energy functionals \[ E_\varepsilon(u):= \int_\Omega \varepsilon|\nabla\nabla u|^2+ {(1-|\nabla u|^2)^2\over\varepsilon} dx \tag{1} \] and contains a relevant progress towards the conjecture that the limiting energy is given by \[ {1\over 3}\int_D |[\nabla u]|^3 d ...
Weimin Jin, Robert V. Kohn
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Singular perturbation methods

1999
Abstract This Chapter is concerned with approximating to the solutions of differential equations containing a small parameter E in what might be called difficult cases where, for one reason or another, a straightforward expansion of the solution in powers of c is unobtainable or unusable.
D W Jordan, P Smith
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Singular Perturbations in Manufacturing

SIAM Journal on Control and Optimization, 1993
Summary: An asymptotic analysis for a large class of stochastic optimization problems arising in manufacturing is presented. A typical example of the problems considered in this paper is a production planning problem with random capacity and demand.
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Perturbation determinants for singular perturbations

Russian Journal of Mathematical Physics, 2014
Let A be a densely defined symmetric operator and let {Ae0 , Ae} be an ordered pair of proper extensions of A such that their resolvent difference is of trace class. We study the perturbation determinant ∆Ae0/Ae(·) of the singular pair {Ae0 , Ae} by using the boundary triplet approach.
Malamud, Mark M., Neidhardt, Hagen
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Singular Perturbation Problems with a Singularity of the Second Kind

SIAM Journal on Mathematical Analysis, 1983
The authors study a singular perturbation problem for the system of ordinary differential equations \[ (\Sigma_{\epsilon})\epsilon y'=t^{\alpha}h(y,z,t,\epsilon);\quad \alpha >-1,\quad z'=t^{\alpha}g(y,z,t,\epsilon);\quad t\in [1,+\infty [ \] the system being quasilinear in the sense of Ringhofer. The problem \(P_{\epsilon}\) investigated is a boundary
Markowich, Peter A., Ringhofer, Christian A.   +1 more
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Singular Perturbation of Linear Systems with a Regular Singularity

Journal of Dynamical and Control Systems, 2002
The paper is devoted to the study of singularly perturbed inhomogeneous linear systems of the form \[ \varepsilon zx'= A(z,\varepsilon) x- f(z,\varepsilon), \] having a regular singularity at the origin. Summability properties of the unique formal solution, which is a power series with respect to the variable \(z\) and the perturbation parameter ...
Balser, W., Kostov, V.
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Corner singularities and singular perturbations

ANNALI DELL UNIVERSITA DI FERRARA, 2001
Summary: A corner singularity expansion is developed for a singularly perturbed elliptic boundary value problem. The problem is set in a sector of the plane. In the expansion, particular attention is paid to the singular perturbation parameter. The result is used to give pointwise bounds on derivatives of the solution.
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Singular singular-perturbation problems

1977
Abstract : Consider initial problems for nonlinear singularly perturbed systems of the form epsilon sub z dot = f(z,t,epsilon) in the singular situation that f sub z(z,t,0) has a nontrivial null space. Under appropriate hypotheses, such problems have asymptotic solutions as epsilon approaches 0 for t or = 0 consisting of the sum of a function of t and ...
R. E. O'Malley, J. E. Flaherty
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Homogenization of a Singular Perturbation Problem

Journal of Mathematical Sciences, 2019
The authors investigate the passage to the homogenization limit done simultaneously with the passage to the limit in yet another independent parameter. Under suitable assumptions and choices of the ordering between the two small parameters, the authors are able to show that there is a case when the limit (weak) solution satisfies a standard Bernoulli ...
Kim, S., Shahgholian, H.
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