Cross-diffusion systems with excluded volume effects and asymptotic gradient flows [PDF]
, 2016 In this paper we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived by Bruna and Chapman from a stochastic system of interacting Brownian particles using the method of matched asymptotic expansions.
Bruna, Maria +3 more
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Quasisolitons in self-diffusive excitable systems, or Why asymmetric diffusivity does not violate the Second Law [PDF]
, 2016 Solitons, defined as nonlinear waves which can reflect from boundaries or transmit through each other, are found in conservative, fully integrable systems.
Biktashev, V. N., Tsyganov, M. A.
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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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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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Global well-posedness of a conservative relaxed cross diffusion system [PDF]
, 2012 We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form $u_i\to \partial_tu_i-\Delta(a_i(\tilde{u})u_i)$ where the $u_i, i=1,...,I$ represent $I$ density-functions ...
Lepoutre, Thomas +2 more
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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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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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Pediatric Blood &Cancer, EarlyView.ABSTRACT Background The management of clinically apparent single lesions or oligofocal nephroblastomatosis, a facultative precursor of nephroblastoma, remains debated. Methods We retrospectively analyzed 37 patients with clinically apparent single or oligofocal nephroblastomatosis (two to three lesions per kidney) among 2347 patients registered between
Nils Welter +17 more
wiley +1 more source
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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Influence of cross-diffusion on the fecally-orally epidemic model with spatial heterogeneity
Advances in Difference Equations, 2017 A strongly coupled cooperative parabolic system, which describes fecally-orally epidemic model with cross-diffusion in a heterogeneous environment, was formulated and analyzed.
Jing Ge, Zhigui Lin, Qunying Zhang
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