Theory of Singular Perturbations in the Case of Spectral Singularities of the Limit Operator

Abstract

Temperature dependences of the high-field electron trapping in a Si02 thin film for temperature ranging from 100 to 423K are investigated. It is found that in the investigated temperature range, when the temperature decreases the effective surface density of the electron traps in the film decreases; the energy levels of the effective electron traps at high field concentrate at very narrow energy range. The thermal generation rateis found to be 1 . 2 8 3~l O '~/ c m~. K andits activation energyis 0.192eV. Based on these results, a model for the electron traps generated at high field in thin oxide is proposed.

A solution of the singularly perturbed Cauchy problem in the presence of a “weak” turning point at the limit operator

“…Отметим работы [2], [3] и [4], посвященные построению асимптотики решения сингулярно возмущенных задач Коши при наличии спектральных особенностей у предельного оператора.…”

“…Новизна представленной работы состоит в том,что методом регуляризации строится глобальная регуляризованная асимптотика на всем отрезке [ 0, T ] неоднородной задачи Коши с произвольными начальными условиями. Наши исследования являются развитием работы [2], в которой описана методика построения регуляризованного асимптотического решения для задач с нестабильным спектром с «простой» точкой поворота, т.е. ситуации, в которой собственные значения в отдельных точках обращаются в нуль (как сказано в [2] "предельный оператор дискретно необратим" ).…”

Regularized Solution of Singularly Perturbed Cauchy Problem in the Presence of Rational “Simple” Turning Point in Two-Dimensional Case

“…A "simple" pivot point of a limit operator (matrix A(τ)) is understood when one eigenvalue vanishes at one point (i.e., matrix A(τ) is irreversible at this point). In [1], the case was considered of when one of the eigenvalues that had the form τ n a(τ), a(τ) = 0, n was natural; in [2] the features of the solution were identified and described for a rational "simple" turning point in the one-dimensional case (when the eigenvalue had the form τ m/n a(τ), a(τ) = 0).…”

“…The fourth part describes the formalism of the Lomov regularization method [1,3,4] that allows one to construct an asymptotic solution uniform over the entire segment [0, T], under additional conditions on the parameters of a singularly perturbed problem, and its right side is the exact solution. The idea of this paper goes back to [1], in which methods were developed for solving a singularly perturbed Cauchy problem in the case of a "simple" turning point of a limit operator with a natural exponent. A lemma is given on the estimation of basic singular functions, a theorem on the point solvability of iterative problems is proved, and the leading term of the asymptotic behavior of a singularly perturbed Cauchy problem is written out.…”

Internal boundary layer for integral-differential equations with zero spectrum of the limit operator and rapidly changing kernel

“…For solutions the asymptotic of the boundary layer type was established. Singularly perturbed systems with irreversible limit operator in the case, when the eigenvalues are purely imaginary, were considered in [1,2,4,7,19,20,21], by the regularization method of S.A.Lomov [14].…”