Integrable Singular Integral Evolution Equations

1993 ◽  
pp. 147-177 ◽  
Author(s):  
P. M. Santini
Keyword(s):  
Singular Integral ◽  
Evolution Equations

scholarly journals Boundedness of Singular Integral Operators with Operator-Valued Kernels and Maximal Regularity of Sectorial Operators in Variable Lebesgue Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Qinghua Zhang ◽  
Yueping Zhu ◽  
Feng Wang
Keyword(s):  
Singular Integral ◽  
Evolution Equations ◽  
Maximal Regularity ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Lebesgue Spaces ◽  
Sectorial Operators ◽  
Variable Lebesgue Spaces ◽  
Scalar Type ◽  
Semilinear Evolution Equations

This paper is devoted to the maximal regularity of sectorial operators in Lebesgue spaces Lp⋅ with a variable exponent. By extending the boundedness of singular integral operators in variable Lebesgue spaces from scalar type to abstract-valued type, the maximal Lp⋅−regularity of sectorial operators is established. This paper also investigates the trace of the maximal regularity space E01,p⋅I, together with the imbedding property of E01,p⋅I into the range-varying function space C−I,X1−1/p⋅,p⋅. Finally, a type of semilinear evolution equations with domain-varying nonlinearities is taken into account.

scholarly journals The Parabolic Transform and Some Singular Integral Evolution Equations

2020 ◽  
Vol 8 (4) ◽  
pp. 410-415
Author(s):  
Mahmoud M. El-Borai ◽  
Khairia El-Said El-Nadi
Keyword(s):  
Singular Integral ◽  
Evolution Equations

Dichotomy theorems for evolution equations

2008 ◽  
Author(s):  
Alexandru Alin Pogan
Keyword(s):  
Evolution Equations ◽  
Dichotomy Theorems

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna

Multi-parameter Singular Integrals II: General Theory

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
General Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Main Issue

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize to the multi-parameter situation. To deal with this, strengthened cancellation conditions are introduced. This is done in two different ways, resulting in four total definitions for singular integral operators (the first two use the strengthened cancellation conditions, while the later two are generalizations of the later two parts of the trichotomy). Thus, we obtain four classes of singular integral operators, denoted by A1, A2, A3, and A4. The main theorem of the chapter is A1 = A2 = A3 = A4; i.e., all four of these definitions are equivalent. This leads to many nice properties of these singular integral operators.

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.

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

Approximate Solution Of A Singular Integral Equation With A Multiplicative Cauchy Kernel In The Half-Plane

2008 ◽  
Vol 8 (2) ◽  
pp. 143-154 ◽  
Author(s):  
P. KARCZMAREK
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Half Plane ◽  
Singular Integral ◽  
Trigonometric Polynomials ◽  
Cauchy Kernel

AbstractIn this paper, Jacobi and trigonometric polynomials are used to con-struct the approximate solution of a singular integral equation with multiplicative Cauchy kernel in the half-plane.

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