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Traveling front of polyhedral shape for a nonlocal delayed diffusion equation
Electronic Journal of Qualitative Theory of Differential Equations, 2020 This paper is concerned with the existence and stability of traveling fronts with convex polyhedral shape for nonlocal delay diffusion equations. By using the existence and stability results of V-form fronts and pyramidal traveling fronts, we first show ...
Jia Liu
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Complexity, 2022 In this paper, we study the existence of positive steady states for a nonlocal reaction-diffusion model which describes the growth of a single phytoplankton species with nonlocal crowding effect caused by chemosensory aggregation in a water column.
Yan Wang, Jinxiang Wang, Xiaobin Yao
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Effective nonlocal kernels on reaction–diffusion networks
Journal of Theoretical Biology, 2021 A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel"
Shin-Ichiro Ei +4 more
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Numerical modeling of population 2D-dynamics with nonlocal interaction [PDF]
Компьютерные исследования и моделирование, 2010 Numerical solutions for the two-dimensional reaction-diffusion equation with nonlocal nonlinearity are obtained. The solutions reveal formation of dissipative structures.
Aleksei Vladimirovich Borisov +2 more
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Axioms, 2023 In this paper, we introduce the Crowley–Martin functional response and nonlocal competition into a reaction–diffusion immunosuppressive infection model.
Yuan Xue, Jinli Xu, Yuting Ding
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Identification of the Diffusion Parameter in Nonlocal Steady Diffusion Problems [PDF]
Applied Mathematics & Optimization, 2015 The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the control and the parameter function as the control variable.
D'Elia, M., Gunzburger, M.
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Journal of Mathematical Analysis and Applications, 2015 In this paper, the authors are concerned with the existence of solutions to nonlocal parabolic partial differential equations, in the sense of aiming to construct solutions that inherit a certain minimizing property. Such parabolic minimizers or variational solutions are advantageous since they are likely to possess better regularity properties due to ...
Bögelein, Verena +3 more
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Fractal and FractionalUltrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge ...
Wei Xu +3 more
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A Nonlocal Fractional Peridynamic Diffusion Model
Fractal and Fractional, 2021 This paper proposes a nonlocal fractional peridynamic (FPD) model to characterize the nonlocality of physical processes or systems, based on analysis with the fractional derivative model (FDM) and the peridynamic (PD) model.
Yuanyuan Wang +4 more
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Nonlocal-in-Time Dynamics and Crossover of Diffusive Regimes
International Journal of Numerical Analysis and Modeling, 2023 The aim of this paper is to study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance.
Qiang Du 0001, Zhi Zhou 0002
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