scholarly journals Global existence of solutions in invariant regions for reaction-diffusion systems with a balance law and a full matrix of diffusion coefficients

2003 ◽  
pp. 1-10 ◽  
Author(s):  
Said Kouachi
Keyword(s):  
Global Existence ◽  
Diffusion Coefficients ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Full Matrix ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems ◽  
Invariant Regions

scholarly journals Invariant Regions and Global Existence of Solutions for Reaction-Diffusion Systems with a Tridiagonal Matrix of Diffusion Coefficients and Nonhomogeneous Boundary Conditions

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Abdelmalek Salem
Keyword(s):  
Global Existence ◽  
Diffusion Coefficients ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Nonhomogeneous Boundary ◽  
Diffusion Systems ◽  
Invariant Regions ◽  
Nonhomogeneous Boundary Conditions

The purpose of this paper is the construction of invariant regions in which we establish the global existence of solutions for reaction-diffusion systems (three equations) with a tridiagonal matrix of diffusion coefficients and with nonhomogeneous boundary conditions after the work of Kouachi (2004) on the system of reaction diffusion with a full 2-square matrix. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of polynomial growth.

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.

Weakly invariant regions for reaction—diffusion systems and applications

2000 ◽  
Vol 130 (5) ◽  
pp. 1165-1180 ◽  
Author(s):  
Si Ning Zheng
Keyword(s):  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Chemical Processes ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems ◽  
Invariant Regions ◽  
Semilinear Parabolic

The important theory of invariant regions in reaction-diffusion equations has only restricted applications because of its strict requirements on both the reaction terms and the regions. The concept of weakly invariant regions was introduced by us to admit wider reaction-diffusion systems. In this paper we first extend the L∞ estimate technique of semilinear parabolic equations of Rothe to the more general case with convection terms, and then propose more precise criteria for the bounded weakly invariant regions. We illustrate, by three model examples, that they are very convenient for establishing the global existence of solutions for reaction-diffusion systems, especially those from ecology and chemical processes.

Influence of mixed boundary conditions in some reaction–diffusion systems

1997 ◽  
Vol 127 (5) ◽  
pp. 1053-1066 ◽  
Author(s):  
Robert H. Martin ◽  
Michel Pierre
Keyword(s):  
Global Existence ◽  
Polynomial Growth ◽  
Existence Of Solutions ◽  
Mixed Boundary ◽  
Reaction Diffusion ◽  
Mixed Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems

SynopsisWe analyse global existence of solutions to a system of two reaction–diffusion equations for whicha ‘balance’ law holds. The main aim is to make clear the influence of different combinations ofboundary conditions on global existence under the assumption that the nonlinearities satisfy polynomial growth estimates.

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