scholarly journals Pseudo Differential Equations, Singular Integrals, and Distributions

2015 ◽  
Vol 1 (1) ◽  
pp. 3-16
Author(s):  
Vladimir Vasilyev
Keyword(s):  
Differential Equations ◽  
Singular Integrals

Multi-parameter Singular Integrals. (AM-189)

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Partial Differential Equations ◽  
Graduate Students ◽  
General Theory ◽  
Differential Equations ◽  
Singular Integrals ◽  
Main Tool ◽  
Classical Theorem ◽  
Quantitative Version ◽  
Linear Partial Differential Equations

This book develops a new theory of multi-parameter singular integrals associated with Carnot–Carathéodory balls. The book first details the classical theory of Calderón–Zygmund singular integrals and applications to linear partial differential equations. It then outlines the theory of multi-parameter Carnot–Carathéodory geometry, where the main tool is a quantitative version of the classical theorem of Frobenius. The book then gives several examples of multi-parameter singular integrals arising naturally in various problems. The final chapter of the book develops a general theory of singular integrals that generalizes and unifies these examples. This is one of the first general theories of multi-parameter singular integrals that goes beyond the product theory of singular integrals and their analogs. This book will interest graduate students and researchers working in singular integrals and related fields.

scholarly journals Integro-differential equations with singular and hypersingular integrals

2019 ◽  
Vol 54 (4) ◽  
pp. 404-407 ◽  
Author(s):  
E. I. Zverovich ◽  
A. P. Shilin
Keyword(s):  
Differential Equations ◽  
Complex Plane ◽  
Singular Integrals ◽  
Closed Curve ◽  
Special Structure ◽  
Finite Part ◽  
Hypersingular Integrals ◽  
Hadamard Finite Part

Quadrature linear integro-differential equations on a closed curve located in the complex plane are solved. The equations contain singular integrals which are understood in the sense of the main value and hypersingular integrals which are understood in the sense of the Hadamard finite part. The coefficients of the equations have a special structure.

scholarly journals Solving Partial Integro-Differential Equations with Weakly Singular Kernel

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Amina Kassim Hussain
Keyword(s):  
Differential Equations ◽  
Singular Integrals ◽  
Numerical Algorithms ◽  
Basis Functions ◽  
Singular Kernel ◽  
Science And Engineering ◽  
Weakly Singular Kernel ◽  
Weakly Singular ◽  
Radial Basis ◽  
Discretization Process

Equations with a combination of integrals and derivatives are known as integro-differential equations. They are a combination of science and engineering. Many models are implemented with the help of integro-differential equations. Various techniques are available to solve integro-differential equations. In the present study, the Radial Basis Function and Adomain Decomposition Method-based numerical algorithms are used to solve a linear partial integro-differential equation with weakly singular kernel, which arises from viscoelasticity. In the discretization process, singular integrals were compared with the product trapezoidal method. Implementation of various radial basis functions was carried out. The proposed system was found to be useful and to provide reproducible results.

Partial Differential Equations

2020 ◽  
Author(s):  
A. K. Nandakumaran ◽  
P. S. Datti
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential
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