Results 201 to 210 of about 37,564 (233)

Nonlocal electrical diffusion equation

International Journal of Modern Physics C, 2016
In this paper, we present an analysis and modeling of the electrical diffusion equation using the fractional calculus approach. This alternative representation for the current density is expressed in terms of the Caputo derivatives, the order for the space domain is [Formula: see text] and for the time domain is [Formula: see text].
J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, V. H. Olivares-Peregrino, M. Benavides-Cruz, C. Calderón-Ramón   +4 more
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Nonlocal reaction—diffusion equations and nucleation

IMA Journal of Applied Mathematics, 1992
Summary: A nonlocal reaction-diffusion equation is presented and analysed using matched asymptotic expansions and multiple timescales. The problem models a binary mixture undergoing phase separation. The particular form of the equation is motivated by arguments from the calculus of variations, with the nonlocality arising from an enforcement of ...
Rubinstein, Jacob, Sternberg, Peter
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Nonlocal Reaction–Diffusion Equations in Biomedical Applications

Acta Biotheoretica, 2022
Nonlocal reaction-diffusion equations describe various biological and biomedical applications. Their mathematical properties are essentially different in comparison with the local equations, and this difference can lead to important biological implications.
Banerjee, M., Kuznetsov, M., Udovenko, O., Volpert, Vitaly   +3 more
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Nonlocal Diffusion in Fractured Rocks

SPE Reservoir Evaluation & Engineering, 2016
Summary Space–time fractional diffusion in a linear, bounded region is considered. An analytical expression for the pressure distribution in the bounded region is derived in terms of the Mittag-Leffler function and the Laplace transformation. Comparisons with numerical solutions indicate excellent agreement.
R.. Raghavan, C.. Chen, J. J. DaCunha
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Nonlocal Reaction-diffusion Equations

2014
We introduced nonlocal reaction-diffusion equations in Section 2.4 of Chapter 1 by means of the model of competition of species. It is also possible to view them in a different way. If individuals of some population consume resources in some area around their average position, then we need to take into account this nonlocal consumption of resources in ...
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Nonlinear Nonlocal Reaction-Diffusion Equations

2014
Let \(\varOmega \subset \mathbb{R}^{N}\), and J be a nonnegative function defined in Ω ×Ω. We consider the problem $$\displaystyle\begin{array}{rcl} \left \{\begin{array}{ll} u_{t}(x,t)& =\int _{\varOmega }J(x,y)u(y,t)\mathit{dy} - h(x)u(x,t) + f(x,u(x,t)),\,x \in \varOmega,\;t > 0 \\ u(x,0) & = u_{0}(x),\quad x \in \varOmega,\end{array} \right.& &{
Aníbal Rodríguez-Bernal, Silvia Sastre-Gómez   +1 more
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Nonlocal diffusivity: Impact on transient transport studies

Physics of Plasmas, 1995
Nonlocal effects are observed in a number of transient transport studies in tokamaks and stellarators. In this paper some consequences of nonlocality are discussed on the basis of a heuristic model for the electron heat diffusivity (χe). The main consequence is the presence of an additional (‘‘missing’’) heating power term (p̃χ) in the heat transport ...
A Jacchia, P Mantica, F De Luca, P Galli, G Gorini   +4 more
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Nonlocal nonlinear advection-diffusion equations

Chinese Annals of Mathematics, Series B, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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THE SINGULARLY PERTURBED NONLOCAL REACTION DIFFUSION SYSTEM

Acta Mathematica Scientia, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mo, Jiaqi, Han, Xianglin, Chen, Songlin
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Blow-up in Nonlocal Reaction-Diffusion Equations

SIAM Journal on Mathematical Analysis, 1998
The author presents blow-up results for reaction-diffusion equations with nonlocal nonlinearities of the following general form \[ u_{t}-\Delta u=F^{t}(R^{t}u)(x),\quad t>0,\quad x\in\Omega, \] where, for each \(t>0\), \(F^{t}: C([0,t]\times \overline\Omega)\to C(\overline\Omega)\), and the past time restriction operator \(R^{t}\) is defined by \(R^{t ...
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