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Mathematics
Wenyuan Ma, Baoqiang Yan
Summary: This paper studies a nonlinear nonlocal parabolic system with nonlinear heat-loss boundary conditions, which are relevant to the thermal explosion model. The paper first proves a comparison principle for certain types of parabolic systems with nonlinear boundary conditions. Based on this, a new theorem for sub-and-super solutions is improved. The paper then presents sufficient conditions for the existence and blow-up of uniformly in finite time solutions based on the new theorem. Additionally, the paper generalizes some lemmas related to uniform blow-up solutions and provides numerical simulations to illustrate the existence and uniform blow-up of solutions.
Article
Mathematics, Applied
Jaewook Ahn, Myeongju Chae, Jihoon Lee
Summary: The study investigates a model with two types of nonlocal cell-cell adhesion, proving the global-in-time well-posedness of the solution and obtaining the uniform boundedness of the solution in a multidimensional bounded domain with no-flux conditions.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
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Mathematics, Applied
Lei Li, Mingxin Wang
Summary: This paper investigates nonlocal diffusion problems with free boundaries, establishing the existence and uniqueness of local solutions using ODE basic theory and the contraction mapping principle. It provides a complete classification for global existence and finite time blow-up of solutions, as well as estimates of blow-up rate and time for the blow-up solution.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics, Applied
Weerawat Sudsutad, Chatthai Thaiprayoon, Sotiris K. Ntouyas
Summary: This paper discusses the existence, uniqueness, and stability of boundary value problems for psi-Hilfer fractional integro-differential equations with mixed nonlocal boundary conditions. The uniqueness result is proved using Banach's contraction mapping principle, and the existence results are established using the Krasnosel'skii's fixed point theorem and the Leray-Schauder nonlinear alternative. Further, four different types of Ulam's stability are studied, and some examples are provided to demonstrate the application of the main results.
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Mathematics, Applied
Ewa Zadrzynska, Wojciech M. Zajaczkowski
Summary: The global existence of weak solutions to the Navier-Stokes equations coupled with the heat equation by the external force dependent on temperature has been shown in a cylindrical domain. The problem is considered under boundary slip conditions, with inflow and outflow, and specific boundary conditions for temperature. An estimate is derived showing that inflow and outflow do not tend to vanish as time approaches infinity.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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Mathematics, Applied
Seshadev Padhi, B. S. R. Prasad, Divya Mahendru
Summary: This study investigates the existence, uniqueness, and multiplicity of positive solutions for a system of Riemann-Liouville fractional differential equations with multipoint boundary conditions, utilizing Schauder's and Avery Henderson fixed point theorem to prove the results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematical & Computational Biology
Debao Yan
Summary: This article presents the existence outcomes of a family of singular nonlinear differential equations containing Caputo's fractional derivatives with nonlocal double integral boundary conditions. The problem is converted into an equivalent integral equation using the nature of Caputo's fractional calculus, and two standard fixed theorems are employed to prove its uniqueness and existence results. An example is provided at the end of the paper to illustrate the obtained results.
MATHEMATICAL BIOSCIENCES AND ENGINEERING
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Mathematics, Applied
Ravi P. Agarwal, Bashir Ahmad, Hana Al-Hutami, Ahmed Alsaedi
Summary: This paper addresses the existence of solutions for a nonlinear multi-term impulsive fractional q-integro-difference equation with nonlocal boundary conditions. The appropriated fixed point theorems are utilized to establish the existence and uniqueness results for the given problem. The obtained results are illustrated through examples.
Article
Mathematics, Applied
Sergey Smirnov
Summary: This study investigates the existence of multiple positive solutions for a nonlinear third-order differential equation under various nonlocal boundary conditions. The boundary conditions examined include Stieltjes integral and special cases of m-point conditions and integral conditions. The main tool used in the proof is Krasnosel'skii's fixed point theorem. To demonstrate the applicability of the findings, examples are provided.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2023)
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Mathematics, Applied
Nguyen Anh Triet, Le Thi Phuong Ngoc, Alain Pham Ngoc Dinh, Nguyen Thanh Long
Summary: This paper focuses on a nonlinear wave equation with initial conditions and nonlocal boundary conditions, proving the existence of a unique weak solution and a unique global solution under certain conditions, with the solution exhibiting exponential energy decay as t approaches positive infinity.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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Mathematics, Applied
Mona Alsulami
Summary: This study investigates the existence of solutions for a nonlinear third-order ordinary differential equation with non-separated multi-point and nonlocal Riemann-Stieltjes boundary conditions. Fixed point theorems and Bohnenblust-Karlin theorem are applied to prove the existence and uniqueness of solutions. Examples are provided to clarify the reported results.
Article
Mathematics
Alexander Gladkov
Summary: In this paper, we investigate the initial boundary value problem for a nonlinear nonlocal parabolic equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We establish the comparison principle, global existence, and blow-up of solutions.
MONATSHEFTE FUR MATHEMATIK
(2023)
Article
Mathematics, Interdisciplinary Applications
Bashir Ahmad, Manal Alnahdi, Sotiris K. Ntouyas
Summary: In this study, a new notion of nonlocal closed boundary conditions is presented. By applying these conditions, the existence of solutions for a mixed nonlinear differential equation involving a right Caputo fractional derivative operator and left and right Riemann-Liouville fractional integral operators of different orders is discussed. A decent and fruitful approach of fixed point theory is employed to establish the desired results. Examples are provided to illustrate the main findings. The paper concludes with some interesting observations.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
Ahmad Y. A. Salamooni, D. D. Pawar
Summary: This paper utilizes fixed point theorems in Banach space to study the existence and uniqueness results of Hilfer-Hadamard-type fractional differential equations on the interval (1,e], with nonlinear boundary conditions included.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Songsong Ji, Gang Pang, Xavier Antoine, Jiwei Zhang
Summary: The proposed method presents a general approach to construct exact artificial boundary conditions for the one-dimensional nonlocal Schrodinger equation by semi-discretizing the equation spatially and developing an accurate numerical method for computing the Green's function. The numerical results demonstrate the accuracy of the boundary conditions and the potential application of the method to other nonlocal models and higher dimensions.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Biology
Andreas Buttenschon, Thomas Hillen, Alf Gerisch, Kevin J. Painter
JOURNAL OF MATHEMATICAL BIOLOGY
(2018)
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Ecology
Andrew W. Bateman, Andreas Buttenschon, Kelley D. Erickson, Nathan G. } Marculis
THEORETICAL ECOLOGY
(2017)
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Biology
Andreas Buttenschon, Leah Edelstein-Keshet
JOURNAL OF MATHEMATICAL BIOLOGY
(2019)
Article
Mathematics, Applied
Andreas Buttenschoen, Theodore Kolokolnikov, Michael J. Ward, Juncheng Wei
EUROPEAN JOURNAL OF APPLIED MATHEMATICS
(2020)
Article
Biology
Andreas Buttenschon, Yue Liu, Leah Edelstein-Keshet
BULLETIN OF MATHEMATICAL BIOLOGY
(2020)
Review
Biochemical Research Methods
Andreas Buttenschon, Leah Edelstein-Keshet
PLOS COMPUTATIONAL BIOLOGY
(2020)
Article
Biology
Andreas Buttenschon, Leah Edelstein-Keshet
Summary: The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. This process can be explained by reaction-diffusion equations. The article numerically simulated and analyzed two polarity models, finding distinct routes to repolarization and consistent results with biological experiments.
BULLETIN OF MATHEMATICAL BIOLOGY
(2022)
