Global existence for a class of quadratic reaction–diffusion systems with nonlinear diffusions and L1 initial data

2016 ◽  
Vol 138 ◽  
pp. 369-387 ◽  
Author(s):  
Michel Pierre ◽  
Guillaume Rolland
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Nonlinear Diffusions

scholarly journals Global Existence of Solutions to a Class of Reaction–Diffusion Systems on Rn

2021 ◽  
Author(s):  
Salah Badraoui
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Classical Solution ◽  
Space Dimension ◽  
Existence Of Solutions ◽  
Bounded Function ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems

We prove in this work the existence of a unique global nonnegative classical solution to the class of reaction–diffusion systems uttx=aΔutx−guvm,vttx=dΔvtx+λtxguvm, where a>0, d>0, t>0,x∈Rn, n,m∈N∗, λ is a nonnegative bounded function with λt.∈BUCRn for all t∈R+, the initial data u0, v0∈BUCRn, g:BUCRn→BUCRn is a of class C1,dgudu∈L∞R, g0=0 and gu≥0 for all u≥0. The ideas of the proof is inspired from the work of Collet and Xin who proved the same result in the particular case d>a=1, λ=1,gu=u. Moreover, they showed that the L∞-norm of v can not grow faster than Olnlnt for any space dimension.

Global Existence for Quadratic Systems of Reaction-Diffusion

2007 ◽  
Vol 7 (3) ◽  
Author(s):  
Laurent Desvillettes ◽  
Klemens Fellner ◽  
Michel Pierre ◽  
Julien Vovelle
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
A Priori ◽  
Reaction Diffusion ◽  
Quadratic Systems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
L Log L

AbstractWe prove global existence in time of weak solutions to a class of quadratic reaction-diffusion systems for which a Lyapounov structure of L log L-entropy type holds. The approach relies on an a priori dimension-independent L

Global Existence for Reaction-Diffusion Systems Modelling Ignition

1998 ◽  
Vol 142 (3) ◽  
pp. 219-251 ◽  
Author(s):  
Miguel A. Herrero ◽  
Andrew A. Lacey ◽  
Juan J. L. Velázquez
Keyword(s):  
Global Existence ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Systems Modelling
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