Random walk with persistence and external bias

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Publication:2913266

DOI10.1007/BF02476407zbMath1296.82044OpenAlexW2026979923MaRDI QIDQ2913266

C. S. Patlak

Publication date: 26 September 2012

Published in: The Bulletin of Mathematical Biophysics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02476407



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I: Space convergence, On Patlak-Keller-Segel system for several populations: a gradient flow approach, An asymptotic preserving scheme for kinetic models for chemotaxis phenomena, A numerical model for durotaxis, Keller-Segel chemotaxis models: a review, A continuous-time stochastic model of cell motion in the presence of a chemoattractant, Suppression of blow up by a logistic source in 2D Keller-Segel system with fractional dissipation, From individual to collective displacements in heterogeneous environments, Three-dimensional random walk models of individual animal movement and their application to trap counts modelling, Existence and uniqueness of solutions for a hyperbolic Keller-Segel equation, A Turing mechanism in order to explain the patchy nature of Crohn's disease, Generalized travelling wave solutions for hyperbolic chemotaxis PDEs, Existence of a nontrivial steady-state solution to a parabolic-parabolic chemotaxis system with singular sensitivity, On a fully parabolic chemotaxis system with source term and periodic asymptotic behavior, Bi-flux theory applied to the dispersion of particles in anisotropic substratum, Attraction-repulsion taxis mechanisms in a predator-prey model, Finite-time blowup in Cauchy problem of parabolic-parabolic chemotaxis system, Maximal regularity and a singular limit problem for the Patlak-Keller-Segel system in the scaling critical space involving \textit{BMO}, The one-dimensional stochastic Keller-Segel model with time-homogeneous spatial Wiener processes, Well-posedness and unconditional uniqueness of mild solutions to the Keller-Segel system in uniformly local spaces, A new numerical method to solve some \(\mathrm{PDE_s}\) in the unit ball and comparison with the finite element and the exact solution, Impact of the purposeful kinesis on travelling waves, Efficient numerical algorithms based on difference potentials for chemotaxis systems in 3D, Local well-posedness and finite time blow-up of solutions to an attraction-repulsion chemotaxis system in higher dimensions, Pattern formation of a spatial vegetation system with root hydrotropism, Mathematical models for chemotaxis and their applications in self-organisation phenomena, A hybrid mass transport finite element method for Keller-Segel type systems, Odd-even based asymptotic preserving scheme for a 2D stochastic kinetic-fluid model, Fourier analysis of local discontinuous Galerkin methods for linear parabolic equations on overlapping meshes, Nonlinear aggregation-diffusion equations: radial symmetry and long time asymptotics, Neural network approach to data-driven estimation of chemotactic sensitivity in the Keller-Segel model, Boundedness and global existence in the higher-dimensional parabolic -- parabolic chemotaxis system with/without growth source, A nonlocal model describing tumor angiogenesis, Global boundedness in a quasilinear chemotaxis system with signal-dependent sensitivity, A review of the mean field limits for Vlasov equations, Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces, Well-posedness and singularity formation for inviscid Keller-Segel-fluid system of consumption type, On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher, On a class of Keller-Segel chemotaxis systems with cross-diffusion, A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis



Cites Work