Global Existence in Reaction-Diffusion Systems with Control of Mass: a Survey

By Michel Pierre. 2010

314 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Control and Systems Engineering, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/8a039b12ea34732200c7cfa4b9b74249c3fb19dc

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Citations in the corpus

Global existence for reaction–diffusion systems with dissipation of mass and quadratic growth (2018, unknown): “(d) The existence of a global weak solution was shown in [6,16] under the mere Assumptions (3)–(5) (without conservation of mass or dissipation of entropy).”
Improved Duality Estimates and Applications to Reaction-Diffusion Equations (2013, methodology): “A last application of the properties of the heat kernel in 2D and the duality estimate of [21, 23] shows that ai ∈ L −0 T , when i = 1 2 3.”
Global Existence of Renormalized Solutions to Entropy-Dissipating Reaction–Diffusion Systems (2015, background): “In particular, the following questions remain unsolved: • Does our notion of solution guarantee uniqueness? Can a stronger notion of solution be defined sufficient for proving uniqueness? This is probably a difficult problem, as already in the case of solutions which satisfy R(u) ∈ L(1), but u / ∈ L”
Global Existence Analysis of Cross-Diffusion Population Systems for Multiple Species (2016, methodology): “Equation (1) can be written in the form ∂t ui − (ui pi (u)) = fi (u), (5) which allows for the proof of an L2+s estimate by the duality method [8,21], but we will not exploit this method in the paper.”
Solutions of the 4-species quadratic reaction-diffusion system are bounded and C∞-smooth, in any space dimension (2017, background): “We refer the reader to the survey [22] for a general presentation of the problem, further references, and many deep comments on the mathematical difficulties raised by such systems.”