Transport Equations in Biology

By Benoit Perthame. 2006

1,022 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bb3b055d652b5d4952afc57f8b8219731b7ed63b

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In Modeling and Simulation

Citations in the corpus

ON A CHEMOTAXIS MODEL WITH SATURATED CHEMOTACTIC FLUX (2012, background): “A variety of regularizations has been proposed over the past decades, see the review papers [18–20], the monograph [33] and references therein.”
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production (2016, background): “d whenever R Ω u0 is small; as a precise value distinguishing the respective mass regimes either allowing for or suppressing explosions the critical mass mc = 8π could be identiﬁed (cf. [3], [26] and [30] for (1.3) and closely related variants thereof). As for the fully parabolic chemotaxis system (”
Functional inequalities, thick tails and asymptotics for the critical mass Patlak–Keller–Segel model (2010, methodology): “We introduce a strategy of controlled concentration to deal with this issue, and then use the regularity obtained from the entropy-entropy dissipation inequality to prove the existence of basins of attraction for each stationary state composed by certain initial data converging towards ̺λ.”
Some simple but challenging Markov processes (2014, methodology): “ has to consider the PDE ∂tu(x,t) = −∂x(τ(x)u(x,t)) −λ(x)u(x,t) +2 Z∞ x λ(y)β(y,x)u(y,t)dy. This growth-fragmentation equations have been extensively studied from a PDE point of view (see for example [56, 23, 15, 46]). A probabilistic approach is used in [10] to study the pure fragmentation process.”
Stabilization in a two-dimensional chemotaxis-Navier–Stokes system (2013, neutral): “[14], [34], [16], [21], [22] and also [15] and [23] for broader discussions, as well as e.”
Suppression of Chemotactic Explosion by Mixing (2015, background): “We refer to [35], [11], and [12] for more details and further references.”
Delayed blow‐up for chemotaxis models with local sensing (2020, background): “[22, 28]), and we refer to [3, 17, 18, 27, 29] for an overview of the modeling and basic results.”
On dimensionless numbers (2008, background): “Biology and biosystems), related to the material presented in Appendix C: McMahon, 1973, Pilbeam and Gould, 1974, McMahon and Bonner, 1983, Hjortso, 2005, Nopens and Biggs, 2006, Thompson, 1943, Perthame, 2006, Ramkrishna, 2000.”
Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations (2010, background): “The literature on concrete applications is quite large and we refer the reader to [7, 12] as general sources on the topic, and to the references cited in [3, 8, 13] for particular applications.”
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity (2011, methodology): “0 (cf. also [C1] for related results). When the diﬀusion of the chemical signal is considered to occur much faster than that of cells, by the approach of quasi-steady-state approximation (cf. [JL] or [P]), the parabolicparabolic chemotaxis model (0.1) can be reduced to simpliﬁed parabolic-elliptic m”
Diffusive and nondiffusive population models (2010, methodology): “[110] have proved the existence and long-time behavior of solutions to (14)-(15) without using a maximal life span condition (also see [121]).”
Equilibria of homogeneous functionals in the fair-competition regime (2016, methodology): “The two-dimensional logarithmic case (m = 1, k = 0) is the so-called Keller–Segel system in its simplest formulation [35,36,41,33,31,9,43].”