Global Solutions of Some Chemotaxis and Angiogenesis Systems in High Space Dimensions

By Lucilla Corrias, Benoit Perthame, Hatem Zaag. 2004

399 citations recorded by the source corpus.

Subfields: Cell Biology, Modeling and Simulation, Oncology

View Paper: https://www.semanticscholar.org/paper/2961a86ad75e62eb55500afbc3365dd41f26a54d

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Citations in the corpus

Fast Reaction Limit and Large Time Behavior of Solutions to a Nonlinear Model of Sulphation Phenomena (2007, background): “Communications in Partial Differential Equations, 32: 163–189, 2007 Copyright © Taylor & Francis Group, LLC ISSN 0360-5302 print/1532-4133 online DOI: 10.1080/03605300500361438”
Equilibria of homogeneous functionals in the fair-competition regime (2016, background): “It was shown in [30] for linear diffusion m = 1 that global in time weak solutions exist for initial data with small enough LN/2-norm, whereas there are no global smooth solutions with fast decay if the second moment of the initial data is dominated by a power of the mass (with these two conditions ”
A coupled Keller–Segel–Stokes model: global existence for small initial data and blow-up delay (2012, methodology): “In 3D, the critical norm for the Keller-Segel equations is L; see [14].”
Critical mass for a Patlak–Keller–Segel model with degenerate diffusion in higher dimensions (2008, methodology): “We follow a procedure analogous to the ones in [20, 5, 30, 13].”
Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension (2010, neutral): “One available criterion for global existence involves the Ld/2−norm of the initial cell density [18, 19, 20, 36].”
On the parabolic-elliptic Patlak-Keller-Segel system in dimension 2 and higher (2011, background): “In higher dimensions the critical quantity is no longer the mass but the Ld/2-norm, see [29].”
Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations (2011, methodology): “[4] L. Corrias, B. Perthame and H. Zaag, Global solutions of some chemotaxis and angiogenesis systems in high space dimensions, Milan J. Math., 72 (2004), 1–28.”
Well-posedness of a 3D parabolic–hyperbolic Keller–Segel system in the Sobolev space framework (2012, neutral): “[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.”
Uniqueness for Keller-Segel-type chemotaxis models (2012, methodology): “L∞-apriori estimates were obtained in the classical parabolic-elliptic KS equation ε = 0 with d ≥ 2 and α ≥ 0 for small Ld/2 initial data in [20, 21].”
PDE Models for Chemotactic Movements: Parabolic, Hyperbolic and Kinetic (2004, methodology): “However in two space dimensions we have the following result (still obtained in [17]) Theorem 5.”