Results 141 to 150 of about 1,207 (185)

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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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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Singularly perturbed elliptic systems

Nonlinear Analysis: Theory, Methods & Applications, 2006
The authors prove the existence of a family of positive solutions for two coupled nonlinear stationary Schrödinger equations, concentrating at a point in the limit. In some cases the location of the concentration point is given in terms of the potential functions of the stationary Schrödinger equations.
Alves, Claudianor O., Soares, Sérgio H. M.   +1 more
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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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Singularly continuous spectrum of singularly perturbed operators

Nonlinear Oscillations, 2006
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Singularly Perturbed Operators

1994
Let A = A* > 1 be a self-adjoint unbounded operator in a separable complex Hilbert space H.
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Singular Singularly Perturbed Systems

2014
In this chapter we consider singularly perturbed differential systems whose degenerate equations have an isolated but not simple solution. In that case, the standard theory to establish a slow integral manifold near this solution does not work. Applying scaling transformations and using the technique of gauge functions we reduce the original singularly
Elena Shchepakina, Vladimir Sobolev, Michael P. Mortell   +2 more
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Singularly perturbed difference equations

Journal of Difference Equations and Applications, 1999
Comstock and Hsiao have given a method for constructing asymptotic approximations for singularly perturbed linear difference equations with two point boundary conditions and for verifying the corre...
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Singularly perturbed Hopf bifurcation

IEEE Transactions on Circuits and Systems, 1985
Hopf bifurcation is the simplest way in which periodic solutions can emerge from an equilibrium point of an autonomous one-parameter family of ordinary differential equations. The purpose of this paper is to study persistence of the Hopf bifurcation under singular perturbations of vector field.
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