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Mathematics
Valery V. V. Vasiliev, Sergey A. A. Lurie
Summary: This paper addresses the issue of discontinuities in mathematical physics solutions which describe actual processes but are not observed in experiments. The author suggests that the presence of discontinuities is linked to classical differential calculus that analyzes infinitesimal quantities. To overcome this, the paper introduces nonlocal functions and nonlocal derivatives, which are obtained by averaging over small finite intervals of the independent variable instead of using the traditional point approach. By incorporating these nonlocal functions into classical equations and introducing additional equations to connect them with traditional functions, continuous solutions to classical singular problems in mathematical physics are obtained. The approach is demonstrated and supported by experimental data using the problems of a loaded string and circular membrane.
Article
Multidisciplinary Sciences
Michal Beidzinski, Tomasz Galaj, Radoslaw Bednarski, Filip Pietrusiak, Marek Galewski, Adam Wojciechowski
Summary: The article introduces a method to consider the existence of non-spurious solutions in the Dirichlet problem and proposes a new approach to derive a discrete family of approximating problems.
Article
Mathematics, Applied
Roberto Feola, Benoit Grebert, Felice Iandoli
Summary: In this paper, we consider quasilinear, Hamiltonian perturbations of the cubic Schrodinger and the cubic Klein-Gordon equations on the d-dimensional torus. We prove that the lifespan of solutions is strictly larger than the local existence time. Specifically, for the Schrodinger equation, the lifespan is at least of order O(is an element of(-4)), and for the Klein-Gordon equation, the solutions exist for a time of order O(is an element of(-8/3-)), as long as d ≥ 3. In the case of semilinear perturbations for the Klein-Gordon equation, we show that the lifespan is at least of order O(is an element of(-10/3-)), improving on the previous general results.
Article
Mathematics, Applied
Charles Braga Amorim, Marcelo Fernandes de Almeida, Eder Mateus
Summary: This paper investigates the impact of energy dissipation on the global existence of solutions in the Boussinesq system. Specifically, it considers the case when the initial data belongs to scaling invariant function spaces. By introducing appropriate conditions, the paper demonstrates the existence of solutions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Erbol Zhanpeisov
Summary: In this paper, we prove the existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces, covering a wide range of initial data including distributions other than Radon measures. We also establish sufficient conditions for the existence of solutions to viscous Hamilton-Jacobi equations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2023)
Article
Computer Science, Information Systems
R. Beigmohamadi, A. Khastan, J. J. Nieto, R. Rodriguez-Lopez
Summary: In this study, we introduce discrete interval fractional difference equations subject to non-periodic boundary conditions and obtain two types of solutions for these problems under the generalized Hukuhara difference. We then provide explicit expressions of each type of solution for convenience. Further, we investigate the necessary and sufficient conditions for the existence and uniqueness of a non-periodic solution of each specific type using the Banach contraction mapping principle. Finally, we provide an example to illustrate the main result.
INFORMATION SCIENCES
(2023)
Article
Mathematics, Applied
Wenji Chen, Jianfeng Zhou
Summary: This paper investigates the inhomogeneous Doi-Onsager equations with a special viscous stress and proves the global existence of weak solutions in periodic regions. The key element of the proof is demonstrating the convergence of the nonlinear terms, which is reduced to proving the strong compactness of the moment of the family of number density functions. The proof is based on studying the propagation of strong compactness, L2-estimates for a family of number density functions, and energy dissipation estimates.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2021)
Article
Mathematics, Applied
Francescantonio Oliva
Summary: The paper focuses on the existence and uniqueness of nonnegative solutions to a problem modeled by a p-Laplacian operator and nonlinearity. Examples and extensions are discussed at the end of the paper.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2021)
Article
Mathematics, Applied
Svetlin G. Georgiev, Khaled Zennir, Keltoum Bouhali, Rabab Alharbi, Yousif Altayeb, Mohamed Biomy
Summary: In this paper, we study a class of initial value problems for impulsive nonlinear wave equations. We use a new topological approach to prove the existence of at least one and at least two nonnegative classical solutions. To prove our main results, we provide a suitable integral representation of the solutions. Then, we construct two operators such that any fixed point of their sum is a solution.
Article
Astronomy & Astrophysics
Wompherdeiki Khyllep, Andronikos Paliathanasis, Jibitesh Dutta
Summary: The study investigates one of Einstein's alternative formulations based on nonmetricity scalar Q generalized as f(Q) theory, focusing on the power-law form of f(Q) gravity. The analysis reveals that the geometric component of the theory determines the late-time acceleration of the Universe, and the model deviates from ΛCDM even for |n| < 1 at the perturbation level. The integrability of the model is examined using singularity analysis, finding conditions under which field equations pass the Painleve test and possess the Painleve property.
Article
Mathematics
Mohamed El Hichami, Youssef El Hadfi
Summary: In this work, we investigate the existence and regularity of solutions to problems represented by the equation { - Delta pu + u|del u| (p) = f h(u) in Omega, u = 0 on partial derivative Omega }. Here, Omega is an open bounded subset of R-N (N >= 2) with Lipschitz boundary, Delta(p)u represents the p-Laplacian operator, f epsilon L-q( Omega) (q > (N)(p)) is a nonnegative function, and h is a continuous real function that may blow up at zero.
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
(2023)
Article
Mathematics, Applied
Alexandru Tudorache, Rodica Luca
Summary: This study investigates the existence and multiplicity of positive solutions for a system of Riemann-Liouville fractional differential equations with sequential derivatives, positive parameters, and sign-changing singular nonlinearities, under nonlocal uncoupled boundary conditions containing various fractional derivatives and Riemann-Stieltjes integrals. The main existence results are proven using the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel'skii fixed point theorem.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Xiaohua He, Shuibo Huang, Qiaoyu Tian
Summary: This paper considers the effects of singular convection term and lower order term on the existence and regularity of solutions to an elliptic Dirichlet problem. The main results show the combined effects of these two terms on the solution.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Gabriele Bonanno, Pasquale Candito, Donal O'Regan
Summary: The study demonstrates the existence of at least one nontrivial solution for a nonlinear sixth-order ordinary differential equation using critical point theory.
Article
Mathematics
Abbas Moameni, K. L. Wong
Summary: By utilizing a new variational principle, the study proves the existence of weak solution for a nonlocal semilinear elliptic problem, particularly focusing on supercritical cases, and utilizing fractional Sobolev spaces for analysis. This new variational principle allows effective handling of problems beyond standard weakly compact structure. Instead of working on the entire appropriate Sobolev space, this principle enables dealing with the problem on appropriate convex weakly compact subsets.
JOURNAL OF GEOMETRIC ANALYSIS
(2021)
Article
Biology
K. Harley, P. van Heijster, R. Marangell, G. J. Pettet, M. Wechselberger
MATHEMATICAL BIOSCIENCES
(2015)
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Mathematics, Applied
Peter van Heijster, Chao-Nien Chen, Yasumasa Nishiura, Takashi Teramoto
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2018)
Article
Biology
Lotte Sewalt, Kristen Harley, Peter van Heijster, Sanjeeva Balasuriya
JOURNAL OF THEORETICAL BIOLOGY
(2016)
Article
Mathematics, Applied
A. Doelman, P. van Heijster, F. Xie
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2016)
Article
Mathematics, Applied
P. N. Davis, P. van Heijster, R. Marangell
APPLIED NUMERICAL MATHEMATICS
(2019)
Article
Multidisciplinary Sciences
Arjen Doelman, Peter van Heijster, Jianhe Shen
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2018)
Correction
Mathematics, Applied
Peter van Heijster, Chao-Nien Chen, Yasumasa Nishiura, Takashi Teramoto
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics, Applied
Martina Chirilus-Bruckner, Arjen Doelman, Peter van Heijster, Jens D. M. Rademacher
JOURNAL OF NONLINEAR SCIENCE
(2015)
Article
Mathematics, Applied
Martina Chirilus-Bruckner, Peter van Heijster, Hideo Ikeda, Jens D. M. Rademacher
JOURNAL OF NONLINEAR SCIENCE
(2019)
Article
Mathematics, Interdisciplinary Applications
Claudio Arancibia-Ibarra, Jose D. Flores, Graeme Pettet, Peter van Heijster
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2019)
Article
Engineering, Electrical & Electronic
Ammar Dukhan, Dhammika Jayalath, Peter van Heijster, Bouchra Senadji, Jasmine Banks
EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING
(2020)
Article
Biology
Ronel Scheepers, Graeme J. Pettet, Peter van Heijster, Robyn P. Araujo
BULLETIN OF MATHEMATICAL BIOLOGY
(2020)
Article
Mathematics, Applied
Kristen E. Harley, Peter van Heijster, Robert Marangell, Graeme J. Pettet, Timothy Roberts, Martin Wechselberger
SIAM JOURNAL ON APPLIED MATHEMATICS
(2020)
Proceedings Paper
Mathematics
Peter van Heijster, Tasso J. Kaper, Cynthia A. Bradham
NONLINEAR DYNAMICS IN PARTIAL DIFFERENTIAL EQUATIONS
(2015)
