Shock formation in a chemotaxis model
By Zhian Wang, Thomas Hillen. 2008
87 citations recorded by the source corpus.
Subfields: Cell Biology, Modeling and Simulation, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/a8a56f4a98d5432f14492c7d4ff4f9bf5183107e
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Citations in the corpus
- LARGE-TIME BEHAVIOR OF A PARABOLIC-PARABOLIC CHEMOTAXIS MODEL WITH LOGARITHMIC SENSITIVITY IN ONE DIMENSION (2012, methodology): “2) were recently studied in [37, 21, 22] for ε = 0 and in [23] for ε > 0, based on a Hopf-Cole type transformation”
- Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis (2011, background): “4) which was first introduced in [21] for a chemotaxis model proposed in [10] describing the chemotactic movement for non-diffusible chemicals (i.”
- Pattern Formation of the Attraction-Repulsion Keller-Segel System (2013, unknown): “Chemotactic pattern formation observed both experimentally and numerically exhibits rich interesting coherent structures such as aggregate, fruiting bodies, clusters, spirals, spots, rings, labyrinthine pattern, stripes and prorogating waves [1, 4, 11, 14, 16, 31, 55].”
- Initial–boundary value problems for a system of hyperbolic balance laws arising from chemotaxis (2015, background): “[6,8–10,17,18,29,30,32] for blowup criteria, global existence and long-time behavior of classical solutions, and [19–21] for existence and local nonlinear stability of one-dimensional traveling wave solutions.”
- A user’s guide to PDE models for chemotaxis (2009, unknown): “The complimentary case of zero cell diffusion was studied by Dolak and Schmeiser [25] and Wang and Hillen [106].”
- Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity (2013, background): “For (x, t) ∈ R × [0,∞), Wang and Hillen [22] first established the existence of traveling wave solutions of (1.3) for both χ > 0 and χ 0, subject to the initial data (u, v)(x,0) = (u0, v0)(x) → (u±, v±) as x → ±∞, (1.5) where u0(x) 0 and u± 0.”
- Mathematics of traveling waves in chemotaxis --Review paper-- (2012, methodology): “The result for C0 6= 0 still largely remains open except for the case m = 1 which was solved in [83, 47, 48, 49] for ε ≥ 0 and in [9] for ε = 0 by different methods, which will be sketched below.”
- Well-posedness of a 3D parabolic–hyperbolic Keller–Segel system in the Sobolev space framework (2012, background): “[5, 7, 8, 10, 13, 14, 15, 16, 21, 22, 23, 25, 26, 27, 28, 30, 31, 34, 35, 36, 37] for more discussions in this direction.”