Singular Perturbations of Differential Operators

2000 ◽  
Author(s):  
S. Albeverio ◽  
P. Kurasov
Keyword(s):  
Singular Perturbations ◽  
Differential Operators

scholarly journals A Survey of Some Topics Related to Differential Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Denise Huet
Keyword(s):  
Applied Sciences ◽  
Differential Equations ◽  
Boundary Layers ◽  
Singular Perturbations ◽  
Spectral Properties ◽  
Differential Operators ◽  
Inertial Manifolds ◽  
Alphabetical Order ◽  
Linear And Nonlinear ◽  
Young Researchers

This paper is the result of investigations suggested by recent publications and completes the work of Huet, 2010. The topics, which are dealt with, concern some spaces of functions and properties of solutions of linear and nonlinear, stationary and evolution differential equations, namely, existence, spectral properties, resonances, singular perturbations, boundary layers, and inertial manifolds. They are presented in the alphabetical order. The aim of this document and of Huet, 2010, is to be a useful reference for (young) researchers in mathematics and applied sciences.

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

Singular perturbations and time scales in guidance and control of aerospace systems - A survey

2001 ◽  
Vol 24 (6) ◽  
pp. 1057-1078 ◽  
Author(s):  
D. S. Naidu ◽  
Anthony J. Calise
Keyword(s):  
Time Scales ◽  
Singular Perturbations ◽  
Guidance And Control ◽  
Aerospace Systems ◽  
And Control

Pseudo-differential operators involving Fractional Fourier cosine (sine) transform

Filomat ◽  
2017 ◽  
Vol 31 (6) ◽  
pp. 1791-1801
Author(s):  
Akhilesh Prasad ◽  
Manoj Singh
Keyword(s):  
Differential Operators ◽  
Fourier Cosine ◽  
Sine Transform ◽  
Pseudo Differential Operators

Representation of All Maximally Dissipative Multipoint Differential Operators for First Order

2020 ◽  
Vol 41 (9) ◽  
pp. 1854-1863
Author(s):  
R. Öztürk Mert
Keyword(s):  
Differential Operators ◽  
First Order

Spectral Methods

2018 ◽  
Author(s):  
S. G. Rajeev
Keyword(s):  
Simple Model ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Linear Algebra ◽  
Spectral Methods ◽  
Differential Operators ◽  
Higher Dimensions ◽  
Standard Linear ◽  
Sommerfeld Equation ◽  
Spectral Discretization

Thenumerical solution of ordinary differential equations (ODEs)with boundary conditions is studied here. Functions are approximated by polynomials in a Chebychev basis. Sections then cover spectral discretization, sampling, interpolation, differentiation, integration, and the basic ODE. Following Trefethen et al., differential operators are approximated as rectangular matrices. Boundary conditions add additional rows that turn them into square matrices. These can then be diagonalized using standard linear algebra methods. After studying various simple model problems, this method is applied to the Orr–Sommerfeld equation, deriving results originally due to Orszag. The difficulties of pushing spectral methods to higher dimensions are outlined.

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