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Semilinear singular perturbation
Nonlinear Analysis: Theory, Methods & Applications, 1995A second-order periodic boundary value problem is considered. The method of upper and lower solutions is applied to prove the existence of a solution.
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Singular Perturbation Problems
1951The equations considered in this rarer are linear differential equations in one and two independent variables. The problem at hand is to study solutions of boundary value problems for these equations in their dependence on a small parameter ϵ. Specifically, the equations are of the form (A) ϵ Nɸ + Mɸ = 0 where M, N are linear differential expressions,
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Singular Perturbation Problems
2004In this chapter the problems when the small parameter stands by a highest order derivatives are considered. Note that for e = 0 a qualitative change of the system occurs since the system order of the analysed differential equation is decreased. The similar like asymptotics is called the singular one.
I. Andrianov +2 more
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Singular Perturbation Problems
1985An operator L = L(e) depending on a parameter e is called singularly perturbed if the limiting operator \(L(0) = \begin{array}{*{20}{c}} {\lim } \\ {\varepsilon \to 0} \end{array}L(\varepsilon )\) is of a type other than L(e) for e > 0. For instance, an elliptic operator L(e) = e L I + L II (e > 0) is singularly perturbed if L II is non-elliptic or ...
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1988
In this chapter we present the singular perturbation method for continuous and discrete control systems. The boundary-layer method is also discussed where the approximate solution is given by the outer series and a boundary-layer correction which is equivalent to the difference between the inner and inter mediate series.
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In this chapter we present the singular perturbation method for continuous and discrete control systems. The boundary-layer method is also discussed where the approximate solution is given by the outer series and a boundary-layer correction which is equivalent to the difference between the inner and inter mediate series.
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Hyperbolic-parabolic singular perturbations
1993Summary: We discuss a singular perturbations problem for the telegraphist equation with a small parameter and the heat equation in a problem with (some) data given on a general moving boundary. Rigorous and explicit estimates are shown and the uniform convergence is proved.
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1984
In §6.2 in the last chapter we briefly discussed, by way of example, some singular perturbation problems in linear differential equations which could be solved using the exponential method developed there. In this chapter we discuss some more generally applicable singular perturbation techniques.
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In §6.2 in the last chapter we briefly discussed, by way of example, some singular perturbation problems in linear differential equations which could be solved using the exponential method developed there. In this chapter we discuss some more generally applicable singular perturbation techniques.
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