Results 31 to 40 of about 145 (135)

The nonlocal problem for fractal diffusion equation

Міжнародний науково-технічний журнал "Проблеми керування та інформатики", 2023
Over the past few decades, the theory of pseudodifferential operators (PDO) and equations with such operators (PDE) has been intensively developed. The authors of a new direction in the theory of PDE, which they called parabolic PDE with non-smooth ...
Ярослав Михайлович Дрінь, Ірина Ігорівна Дрінь, Світлана Сергіївна Дрінь   +2 more
doaj   +1 more source

Hypersingular Integral Equations Encountered in Problems of Mechanics

Mathematics
In the paper, for hypersingular integral equations with new kernels, a solution is constructed using an approach based on Chebyshev orthogonal polynomials and the principle of contraction mappings.
Suren M. Mkhitaryan, Hovik A. Matevossian, Eghine G. Kanetsyan, Musheg S. Mkrtchyan   +3 more
doaj   +1 more source

Characterization of Riesz and Bessel potentials on variable Lebesgue spaces

Journal of Function Spaces and Applications, 2006
Riesz and Bessel potential spaces are studied within the framework of the Lebesgue spaces with variable exponent. It is shown that the spaces of these potentials can be characterized in terms of convergence of hypersingular integrals, if one assumes that
Alexandre Almeida, Stefan Samko
doaj   +1 more source

Sharp commutator estimates of all order for Coulomb and Riesz modulated energies

Communications on Pure and Applied Mathematics, Volume 79, Issue 2, Page 207-292, February 2026.
Abstract We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super‐Coulomb Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by the second author and collaborators in the study of mean‐field limits and statistical mechanics of ...
Matthew Rosenzweig, Sylvia Serfaty
wiley   +1 more source

Hypersingular Marcinkiewicz Integrals along Surface with Variable Kernels on Sobolev Space and Hardy-Sobolev Space

Journal of Inequalities and Applications, 2011
Let , the authors introduce in this paper a class of the hypersingular Marcinkiewicz integrals along surface with variable kernels defined by , where with .
Li Yin, Wei Ruiying
doaj   +2 more sources

Numerical Modeling of the Recession and Closure of Planar Hydraulic Fractures: Contact‐Based Versus Asymptotic‐Informed Schemes

International Journal for Numerical and Analytical Methods in Geomechanics, Volume 49, Issue 17, Page 4054-4075, 10 December 2025.
ABSTRACT We compare two algorithms to simulate the propagation, arrest, recession, and closure of a planar hydraulic fracture, focusing on their ability to capture the physical processes governing fracture recession and closure. The first algorithm is based on a fixed grid with contact detection during recession, while the second is based on a moving ...
Mohsen Talebkeikhah, Andreas Möri, Anthony Peirce, Emmanuel Detournay, Brice Lecampion   +4 more
wiley   +1 more source

An Automatic Quadrature Schemes and Error Estimates for Semibounded Weighted Hadamard Type Hypersingular Integrals

Abstract and Applied Analysis, 2014
The approximate solutions for the semibounded Hadamard type hypersingular integrals (HSIs) for smooth density function are investigated. The automatic quadrature schemes (AQSs) are constructed by approximating the density function using the third and ...
Sirajo Lawan Bichi, Z. K. Eshkuvatov, N. M. A. Nik Long   +2 more
doaj   +1 more source

Explicit solution of one hypersingular integro-differential equation of the second order

Журнал Белорусского государственного университета: Математика, информатика, 2019
The linear equation on the curve located on the complex plane is studied. The equation contains the desired function, its derivatives of the first and second orders, as well as hypersingular integrals with the desired function.
Andrei P. Shilin
doaj   +1 more source

Fractional Q$Q$‐curvature on the sphere and optimal partitions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara, Juan Carlos Fernández, Alberto Saldaña   +2 more
wiley   +1 more source

Fractional integrals and hypersingular integrals in variable order Hölder spaces on homogeneous spaces

Journal of Function Spaces and Applications, 2010
We consider non-standard Hölder spaces Hλ(⋅)(X) of functions f on a metric measure space (X, d, μ), whose Hölder exponent λ(x) is variable, depending on x ∈ X.
Natasha Samko, Stefan Samko, Boris Vakulov   +2 more
doaj   +1 more source