caa a22 4500 606166351 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s10440-014-9968-y doi (NATIONALLICENCE)springer-10.1007/s10440-014-9968-y Global Existence for a Class of Reaction-Diffusion Systems with Mass Action Kinetics and Concentration-Dependent Diffusivities [Elektronische Daten] [Dieter Bothe, Guillaume Rolland] In this work, we study the existence of classical solutions for a class of reaction-diffusion systems with quadratic growth naturally arising in mass action chemistry when studying networks of reactions of the type A i +A j ⇌A k with Fickian diffusion, where the diffusion coefficients might depend on time, space and on all the concentrations c i of the chemical species. In the case of one single reaction, we prove global existence for space dimensions N≤5. In the more restrictive case of diffusion coefficients of the type d i (c i ), we use an L 2-approach to prove global existence for N≤9. In the general case of networks of reactions we extend the previous method to get global solutions for general diffusivities if N≤3 and for diffusion of type d i (c i ) if N≤5. In the latter quasi-linear case of d i (c i ) and for space dimensions N=2 and N=3, global existence holds for more than quadratic reactions. We can actually allow for more general rate functions including fractional power terms, important in applications. We obtain global existence under appropriate growth restrictions with an explicit dependence on the space dimension N. Springer Science+Business Media Dordrecht, 2014 Reaction-diffusion systems nationallicence Reversible reactions nationallicence Mass action kinetics nationallicence Global existence nationallicence Filtration equation nationallicence Bothe Dieter Nantes, France aut Rolland Guillaume Nantes, France aut Acta Applicandae Mathematicae Springer Netherlands 139/1(2015-10-01), 25-57 0167-8019 139:1<25 2015 139 10440 https://doi.org/10.1007/s10440-014-9968-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9968-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bothe Dieter Nantes, France aut NATIONALLICENCE 700 1- Rolland Guillaume Nantes, France aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 139/1(2015-10-01), 25-57 0167-8019 139:1<25 2015 139 10440