Results 41 to 50 of about 12,187,697 (193)

Expansions of the Solutions of the General Heun Equation Governed by Two‐Term Recurrence Relations for Coefficients

Advances in High Energy Physics, Volume 2018, Issue 1, 2018., 2018
We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from those applied before. In general, the coefficients of the expansions obey three‐term recurrence relations.
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan, Saber Zarrinkamar   +3 more
wiley   +1 more source

Solutionsof Fuzzy Goursat Problems with Generalized Hukuhara (gH)-Differentiability Concept

Axioms
In this manuscript, we will discuss the solutions of Goursat problems with fuzzy boundary conditions involving gH-differentiability. The solutions to these problems face two main challenges.
Noor Jamal, Muhammad Sarwar, Kamaleldin Abodayeh, Manel Hleili, Saowaluck Chasreechai, Thanin Sitthiwirattham   +5 more
doaj   +1 more source

On Bureau's Classification of Quadratic Differential Equations in Two Variables Free of Movable Critical Points

Studies in Applied Mathematics, Volume 155, Issue 2, August 2025.
ABSTRACT As part of the efforts aimed at extending Painlevé and Gambier's work on second‐order equations in one variable to first‐order ones in two, in 1981, Bureau classified the systems of ordinary quadratic differential equations in two variables which are free of movable critical points (which have the Painlevé Property).
Adolfo Guillot
wiley   +1 more source

Singular Solutions to a (3 + 1)‐D Protter‐Morawetz Problem for Keldysh‐Type Equations

Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017
We study a boundary value problem for (3 + 1)‐D weakly hyperbolic equations of Keldysh type (problem PK). The Keldysh‐type equations are known in some specific applications in plasma physics, optics, and analysis on projective spaces. Problem PK is not well‐posed since it has infinite‐dimensional cokernel.
Nedyu Popivanov, Tsvetan Hristov, Aleksey Nikolov, Manfred Schneider, Alexander Iomin   +4 more
wiley   +1 more source

Generalizations of Wendroff Integral Inequalities and Their Discrete Analogues

Abstract and Applied Analysis, 2012
Generalizations of Wendroff type integral inequalities with four dependent limits and their discrete analogues are obtained. In applications, these results are used to establish the stability estimates for the solution of the Goursat problem.
Maksat Ashyraliyev
doaj   +1 more source

Non-classic 3D Goursat Problem for One Hyperbolic Equation with Discontinuous Coefficients

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010
For a differential equation of hyperbolic type with discontinuous coefficients a 3D Goursat problem with nonclassical boundary conditions is considered, which requires no matching conditions.
I. G. Mamedov
doaj   +1 more source

Stochastic Hydrodynamic Velocity Field and the Representation of Langevin Equations

Annalen der Physik, Volume 537, Issue 6, June 2025.
A lumped method is proposed to account for both mean‐field hydrodynamics and stochastic fluctuations within the kinematic equations of motion, providing a regularized formulation of the overdamped approximation. The concept of stochastic realizability in broad sense is introduced based on the spectral properties of the Fredholm operator associated with
Massimiliano Giona, Davide Cocco, Giuseppe Procopio   +2 more
wiley   +1 more source

Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients

Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017
A complete family of solutions for the one‐dimensional reaction‐diffusion equation, uxx(x, t) − q(x)u(x, t) = ut(x, t), with a coefficient q depending on x is constructed. The solutions represent the images of the heat polynomials under the action of a transmutation operator.
Vladislav V. Kravchenko, Josafath A. Otero, Sergii M. Torba, Antonio Scarfone   +3 more
wiley   +1 more source

Unveiling What Makes Saturn Ring: Quantifying the Amplitudes of Saturn's Planetary Normal‐Mode Oscillations and Trends in C‐Ring Properties Using Kronoseismology (VII)

Journal of Geophysical Research: Planets, Volume 130, Issue 4, April 2025.
Abstract Certain spiral density waves in Saturn's rings are generated through resonances with planetary normal modes, making them valuable probes of Saturn's internal structure. Previous research has primarily focused on the rotation rates of these waves. However, other characteristics of these waves also contain valuable information about the planet's
V. M. Afigbo, M. M. Hedman, P. D. Nicholson, R. G. French, C. R. Mankovich, R. G. Jerousek, J. Dewberry   +6 more
wiley   +1 more source

Construction of the Global Solutions to the Perturbed Riemann Problem for the Leroux System

Advances in Mathematical Physics, Volume 2016, Issue 1, 2016., 2016
The global solutions of the perturbed Riemann problem for the Leroux system are constructed explicitly under the suitable assumptions when the initial data are taken to be three piecewise constant states. The wave interaction problems are widely investigated during the process of constructing global solutions with the help of the geometrical structures
Pengpeng Ji, Chun Shen, Ming Mei
wiley   +1 more source