Global Existence for Quadratic Systems of Reaction-Diffusion

By Laurent Desvillettes, Klemens Fellner, Michel Pierre, Julien Vovelle. 2007

128 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/b00e6e71d45949e337155e14bc61360cec68b79f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Genetics

1. Michel Pierre
2. A. Jungel
3. Laurent Desvillettes

In Modeling and Simulation

1. A. Jungel
2. Michel Pierre
3. Laurent Desvillettes
4. Klemens Fellner
5. Alexis Vasseur
6. C. Caputo
7. Thierry Goudon
8. Julian Fischer

In Public Health, Environmental and Occupational Health

1. A. Jungel
2. Laurent Desvillettes
3. Michel Pierre
4. Klemens Fellner
5. Alexis Vasseur
6. C. Caputo
7. Thierry Goudon
8. Dieter Bothe

Citations in the corpus

• Quasi-steady-state approximation for a reaction–diffusion system with fast intermediate (2010, background): “It is known (see [26], [27], [11]) that this implies L(2)-estimates on W .”
• Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds (2008, background): “1) is unknown and that boundedness of the entropy is insufficient to guarantee that the reaction terms belong to L(1) (see [9]).”
• 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).”
• Global Existence in Reaction-Diffusion Systems with Control of Mass: a Survey (2010, methodology): “It has also been exploited in [21], [13] together with the entropy inequality which is valid for most reversible systems like (2.”
• The boundedness-by-entropy principle for cross-diffusion systems (2014, background): “, dn) with smooth functions di = di(x, t) ≥ 0, the global existence of weak solutions was shown in [22].”
• The boundedness-by-entropy method for cross-diffusion systems (2015, background): “, dn) with smooth functions di = di(x, t) ≥ 0, the global existence of weak solutions was shown in [23].”
• Solutions of the 4-species quadratic reaction-diffusion system are bounded and C∞-smooth, in any space dimension (2017, methodology): “We refer the reader on this issue to [11].”