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The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass control, which includes the important cases of mass conservation and mass dissipation. Under these assumptions, the local classical solution is shown to be global, and in the case of mass conservation or mass dissipation, to have the -norm growing at most polynomially in time. Applications include skew-symmetric Lotka-Volterra systems and quadratic reversible chemical reactions.
Keywords: Reaction-diffusion systems, Classical solutions, Global existence, Slowly-growing a-priori estimates, Mass dissipation
Fellner, Klemens 1 ; Morgan, Jeff 2 ; Tang, Bao Quoc 1
@article{AIHPC_2020__37_2_281_0,
author = {Fellner, Klemens and Morgan, Jeff and Tang, Bao Quoc},
title = {Global classical solutions to quadratic systems with mass control in arbitrary dimensions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {281--307},
publisher = {Elsevier},
volume = {37},
number = {2},
year = {2020},
doi = {10.1016/j.anihpc.2019.09.003},
mrnumber = {4072804},
zbl = {1433.35167},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.09.003/}
}
TY - JOUR AU - Fellner, Klemens AU - Morgan, Jeff AU - Tang, Bao Quoc TI - Global classical solutions to quadratic systems with mass control in arbitrary dimensions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 281 EP - 307 VL - 37 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.09.003/ DO - 10.1016/j.anihpc.2019.09.003 LA - en ID - AIHPC_2020__37_2_281_0 ER -
%0 Journal Article %A Fellner, Klemens %A Morgan, Jeff %A Tang, Bao Quoc %T Global classical solutions to quadratic systems with mass control in arbitrary dimensions %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 281-307 %V 37 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2019.09.003/ %R 10.1016/j.anihpc.2019.09.003 %G en %F AIHPC_2020__37_2_281_0
Fellner, Klemens; Morgan, Jeff; Tang, Bao Quoc. Global classical solutions to quadratic systems with mass control in arbitrary dimensions. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 281-307. doi: 10.1016/j.anihpc.2019.09.003
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