scholarly journals Global Existence of Solutions to Reaction-Diffusion Systems with Mass Transport Type Boundary Conditions

2016 ◽  
Vol 48 (6) ◽  
pp. 4202-4240 ◽  
Author(s):  
Vandana Sharma ◽  
Jeff Morgan
Keyword(s):  
Global Existence ◽  
Mass Transport ◽  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems ◽  
Type Boundary ◽  
Transport Type

scholarly journals Global existence of solutions to reaction diffusion systems with mass transport type boundary conditions on an evolving domain

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Vandana Sharma ◽  
Jyotshana V. Prajapat
Keyword(s):  
Mass Transport ◽  
Boundary Conditions ◽  
Existence Of Solutions ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems ◽  
Type Boundary ◽  
Transport Type

<p style='text-indent:20px;'>We consider reaction diffusion systems where components diffuse inside the domain and react on the surface through mass transport type boundary conditions on an evolving domain. Using a Lyapunov functional and duality arguments, we establish the existence of component wise non-negative global solutions.</p>

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.

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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