Results 21 to 30 of about 314,508 (216)
Diffusion, Self-Diffusion and Cross-Diffusion
Journal of Differential Equations, 1996 The following system, which determines steady-state solutions for a corresponding parabolic system, is considered: \[ \begin{aligned} \Delta[(d_1+\alpha_{11}u_1+\alpha_{12}u_2)u_1] &+u_1(a_1-b_1u_1-c_1u_2)=0,\\ \Delta[(d_2+\alpha_{21}u_1+\alpha_{22}u_2)u_2] &+u_2(a_2-b_2u_1-c_2u_2)=0\quad\text{in }\Omega,\end{aligned} \] \[ {\partial u_1\over\partial ...
Lou, Yuan, Ni, Wei-Ming
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Multi-taxis Cross-Diffusion System
, 2022 AbstractMulti-taxis appears in society interactions and cancer treatment. Society interactions can lead to the complex dynamical behavior in biology and even in criminology ([43, 65, 190]).
Yuanyuan Ke, Jing Li, Yifu Wang
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Envelope Quasisolitons in Dissipative Systems with Cross-Diffusion [PDF]
Physical Review Letters, 2011 We consider two-component nonlinear dissipative spatially extended systems of reaction-cross-diffusion type. Previously, such systems were shown to support "quasi-soliton" pulses, which have fixed stable structure but can reflect from boundaries and penetrate each other.
Biktashev, V. N., Tsyganov, M. A.
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Zoology of a non-local cross-diffusion model for two species [PDF]
, 2017 We study a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in Ref.
Carrillo, J. A. +2 more
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Modeling of nonequilibrium cross-diffusion systems
Journal of Physics: Conference Series, 2022 Abstract In this research, we investigate the modeling of cross-diffusion systems that are not in equilibrium. For a particular equation, it is shown that the parameter values exist and have a numerical solution. A source describes the system of equations considered in this study as being based on the majority of physical processes, such
A U Mamatov, A Yu Nurumova
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Existence and uniqueness analysis of a non-isothermal cross-diffusion system of Maxwell-Stefan type
, 2017 In this article we prove local-in-time existence and uniqueness of solution to a non-isothermal cross-diffusion system with Maxwell-Stefan structure.Comment: 6 ...
Hutridurga, Harsha, Salvarani, Francesco
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Domain-growth-induced patterning for reaction-diffusion systems with linear cross-diffusion [PDF]
, 2018 In this article we present, for the first time, domain-growth induced pat- tern formation for reaction-diffusion systems with linear cross-diffusion on evolving domains and surfaces.
Barreira, Raquel, Madzvamuse, Anotida
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An economic cross-diffusion mutualistic model for cities emergence
, 2019 We study an evolution cross-diffusion problem with mutualistic Lotka-Volterra reaction term to modelize the long-term spatial distribution of labor and capital. The mutualistic behavior is deduced from the gradient flow associated to profits maximization.
de-Córdoba, Gonzalo F. +1 more
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Hele-Shaw limit for a system of two reaction-(cross-)diffusion equations for living tissues [PDF]
, 2019 Multiphase mechanical models are now commonly used to describe living tissues including tumour growth. The specific model we study here consists of two equations of mixed parabolic and hyperbolic type which extend the standard compressible porous medium ...
Bubba, Federica +3 more
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Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example [PDF]
, 2004 We have studied properties of nonlinear waves in a mathematical model of a predator-prey system with pursuit and evasion. We demonstrate a new type of propagating wave in this system. The mechanism of propagation of these waves essentially depends on the
Biktashev, V. N. +3 more
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