The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes

By Hans G. Othmer, Thomas Hillen. SIAM Journal on Applied Mathematics, 2000

435 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/9197362c59b00f5a701cc39fd13146e69dd946ad

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Modeling and Simulation

In Molecular Biology

Citations in the corpus

Global Existence for a Kinetic Model of Chemotaxis via Dispersion and Strichartz Estimates (2007, methodology): “…to receptors saturation, but it also is responsible for an asymmetric kernel (in v, v′) which yields the drift term in the Keller–Segel model that is derived in the diffusion limit of equation (1.1), (see Chalub et al., 2004; Hillen and Othmer, 2000; Hwang et al., 2005a,b, 2006; Perthame, 2007).”
Global existence for chemotaxis with finite sampling radius (2006, background): “More details and rigorous justifications can be found in [9], [22], [5].”
MULTICELLULAR BIOLOGICAL GROWING SYSTEMS: HYPERBOLIC LIMITS TOWARDS MACROSCOPIC DESCRIPTION (2007, background): “Subsequent relevant contributions in this area are due to various authors, among others.(23,34,30,15,18,26,16) In these works biological systems are considered for which interactions do not follow classical mechanical rules, and biological activity may play a relevant role in determining the dynamic”
PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic (2004, background): “This involves specific cancellations that hold true for several linear equations arising in biology The existence theory for the nonlinear system (12)-(13) was settled in [13] (thus extending a result in [33] in the linear case) and yields the”
Stochastic switching in biology: from genotype to phenotype (2017, methodology): “It has subsequently been applied to a wide range of problems in biology, including bacterial chemotaxis [87, 128, 200], wave-like behavior in models of slow axonal transport [99, 100, 212], molecular motor-based models of random intermittent search [188, 189], and gene networks [151, 191].”
A user’s guide to PDE models for chemotaxis (2009, methodology): “Briefly, these are (i) arguments based on Fourier’s law and Fick’s law [45], (ii) biased random walk approaches [78], (iii) interacting particle systems [97], (iv) transport equations [2] or [35], and (v) stochastic processes [86].”
Random walk models in biology (2008, background): “…large time-limiting solutions of both processes being the same, due to short-term correlation effects becoming less evident at large time scales (more detailed analysis and discussion can be found in Othmer et al. 1988; Hillen & Othmer 2000; Okubo & Levin 2001; Hillen 2002; Othmer & Hillen 2002).”
Kinetic Models for Chemotaxis and their Drift-Diffusion Limits (2004, background): “In [9] and [18], Othmer and Hillen studied the diffusion limit of equation (4), without and with chemotactic effects, respectively.”