Article
Mathematics, Interdisciplinary Applications
Gabor Maros, Ferenc Izsak
Summary: The numerical solution of fractional-order elliptic problems in bounded domains with inhomogeneous boundary terms and the full-space fractional Laplacian operator is investigated. Convergence analysis for a lower-order boundary element approximation is based on theory for the corresponding continuous problem. Results are confirmed in a numerical experiment.
FRACTAL AND FRACTIONAL
(2021)
Article
Mathematics, Applied
Ismail Kombe, Reyhan Tellioglu Balekoglu
Summary: In this article, the existence of positive solutions to a nonlinear problem is studied by establishing sufficient conditions. The functions V(x), β(x), and the exponents m + p and q are analyzed, and various concrete potentials V(x) are used to demonstrate the application of the main result.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Jiu Liu, Yu Duan, Jia-Feng Liao
Summary: By using variational methods, a class of Nonlinear Elliptic Equations with the Hardy potential and Berestycki-Lions type conditions is studied, and a bound state solution is obtained.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Agnieszka Kalamajska, Anna Maria Kosiorek
Summary: This study focuses on degenerated nonlinear PDE of elliptic type, which includes a degenerated term.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Junior da S. Bessa, Joao Vitor da Silva, Maria N. B. Frederico, Gleydson C. Ricarte
Summary: We obtain global W2,p estimates for viscosity solutions to fully nonlinear elliptic equations, under weaker structural assumptions than convexity and oblique boundary conditions. Our approach uses geometric tangential methods and imports fine regularity estimates from a limiting profile associated with the original second-order equation. Furthermore, we prove that solutions have BMOp type estimates for their second derivatives when f∈BMOp 2 L degrees degrees.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Engineering, Electrical & Electronic
Bastian Seifert, Markus Pueschel
Summary: This research proposes a novel solution based on matrix perturbation theory to address signal processing issues on directed graphs. By adding a small number of edges to a given digraph, the obtained digraph can be diagonalized, leading to an approximate eigenbasis and Fourier transform. The method demonstrates strong scalability and applicability in experiments with random and real world graphs.
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2021)
Article
Computer Science, Interdisciplinary Applications
Jan Nordstrom, Andrew R. Winters
Summary: Boundary conditions and estimates for systems of the nonlinear shallow water equations in two spatial dimensions are derived based on energy and entropy analysis. It is found that the energy method provides more detailed information and is consistent with the entropy analysis. The nonlinear energy analysis reveals the differences between linear and nonlinear analysis and shows that the results from linear analysis may not hold in the nonlinear case. The nonlinear analysis generally requires a different minimal number of boundary conditions compared to the linear analysis, and the magnitude of the flow does not influence the number of required boundary conditions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Huaiyu Jian, Jian Lu, Xu-Jia Wang
Summary: This paper establishes an asymptotic expansion for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary, showing the singularity profile of solutions. It deals with both linear and nonlinear elliptic equations, including fully nonlinear elliptic equations and equations of Monge-Ampere type.
SCIENCE CHINA-MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Evgenii S. Baranovskii, Mikhail A. Artemov
Summary: We study the generalized unsteady Navier-Stokes equations with a memory integral term and prove the existence and uniqueness of a small-data strong solution. We propose a new approach based on operator treatment and the local unique solvability theorem of an operator equation involving isomorphism between Banach spaces with continuously Frechet differentiable perturbations.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics
Marcelo Amaral, Disson dos Prazeres
Summary: We establish optimal boundary regularity results for viscosity solutions to second order fully nonlinear uniformly elliptic equations, obtaining sharp estimates for borderline cases f is an element of L-n(omega) and f is an element of BMO(omega).
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Alberto Boscaggin, Francesca Colasuonno, Colette De Coster
Summary: This study demonstrates the existence of multiple positive BV-solutions to the Neumann problem, influenced by a class of nonlinear functions and specific conditions. The analysis highlights the continuity of solutions and the sufficient conditions for obtaining classical solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Igor I. Skrypnik, Mykhailo V. Voitovych
Summary: In this study, elliptic and parabolic B-1 classes are introduced to generalize the well-known B-p classes of De Giorgi, Ladyzhenskaya, and Ural'tseva with p > 1. These new classes are then applied to demonstrate the pointwise continuity of bounded solutions to elliptic and parabolic equations with nonstandard growth conditions. The approach also covers new cases of variable exponent and (p, q)-phase growth, including the singular-degenerate parabolic case where p < 2 < q.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ravi P. Agarwal, Hana Al-Hutami, Bashir Ahmad
Summary: We present a new class of boundary value problems involving a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. By utilizing standard fixed-point theorems, we establish the existence and uniqueness results for the given problem. We also provide illustrative examples for the obtained results.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Ammar Khanfer, Lazhar Bougo
Summary: This paper establishes an existence theorem for a system of nonlinear fourth-order differential equations with two parameters, subject to specific integral boundary conditions. The functions involved in the equations must satisfy growth conditions for the theorem to hold.
Article
Mathematics
Zaid Laadjal, Qasem M. Al-Mdallal, Fahd Jarad
Summary: In this article, fixed point theorems are used to study the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation involving Caputo fractional derivatives and nonlocal, non-separated boundary conditions. The considered boundary conditions are different from those in existing literature. Additionally, the Adams-type predictor-corrector method is modified to solve specific cases of the system by implicitly implementing the Gauss-Seidel method.
JOURNAL OF MATHEMATICS
(2021)
