Analysis of a parabolic cross-diffusion population model without self-diffusion

By Li Chen, A. Jungel. 2006

184 citations recorded by the source corpus.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/c9533832f128e51ef79f226326b86f20b1c69766

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Citations in the corpus

Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species (2016, methodology): “This situation was considered in [4] for the two-species case, and we sketch the generalization to the n-species case.”
Mathematical analysis and numerical simulation of pattern formation under cross-diffusion (2013, unknown): “We have also found that, as suggested in [12], an alternative strategy for stabilizing”
Analysis of a finite volume method for a cross-diffusion model in population dynamics (2011, methodology): “Using a finite difference scheme, global existence of a weak solution is obtained in [13], and the global existence of a SKT-type model is established in [14] via a positivity-preserving Euler-Galerkin method.”
The boundedness-by-entropy method for cross-diffusion systems (2015, background): “Compared to the results in the literature (in particular [9,15,16,20,33]), we treat not only much more general situations but also simplify the strategy of the existence proof.”
Diffusive and nondiffusive population models (2010, methodology): “This problem is overcome by using a weak compactness result in L due to Yoshida (see Lemma 6 in [22]).”
On the Entropic Structure of Reaction-Cross Diffusion Systems (2014, methodology): “Although many breakthroughs occurred in the mathematical understanding of cross-diffusion systems in the recent years (see [4, 5] and the references therein), the approximation procedure of these systems frequently leads to intricate or technical methods.”
Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates (2015, background): “The existence of global weak solutions are considered in [5, 6].”
The boundedness-by-entropy principle for cross-diffusion systems (2014, background): “The first global existence result without any restriction on the diffusion coefficients (except positivity) was achieved in [29] in one space dimension and in [14, 15] in several space dimensions.”
Pattern formation driven by cross-diffusion in a 2D domain (2012, background): “In [9, 10, 47] global existence and regularity results have”