1.—On the Existence of Solutions of a Nonlinear Differential Diffusion System.

1972 ◽  
Vol 71 (1) ◽  
pp. 1-7
Author(s):  
C. F. Lee
Keyword(s):  
Differential System ◽  
Diffusion Coefficients ◽  
Existence Of Solutions ◽  
Diffusion System ◽  
Differential Diffusion

SynopsisThe existence and the properties of the solutions of a nonlinear differential system describing a diffusion system with concentration-dependent diffusion coefficients are investigated. It is shown that there exists at least one solution which is monotonie decreasing and asymptotically tends to the prescribed value.

On a reaction–diffusion system modelling infectious diseases without lifetime immunity

2021 ◽  
pp. 1-25
Author(s):  
HONG-MING YIN
Keyword(s):  
Diffusion Coefficients ◽  
A Priori ◽  
Main Tool ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Sobolev Embedding ◽  
System Modelling ◽  
Strongly Coupled ◽  
Elliptic And Parabolic Equations

In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.

scholarly journals Differential Diffusivity Effects in Reactive Convective Dissolution

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 83 ◽  
Author(s):  
V. Loodts ◽  
H. Saghou ◽  
B. Knaepen ◽  
L. Rongy ◽  
A. De Wit
Keyword(s):  
Diffusion Coefficients ◽  
Reaction Rate ◽  
Chemical Species ◽  
Mixing Zone ◽  
Simultaneous Presence ◽  
Dynamic Effects ◽  
Density Profiles ◽  
Differential Diffusion ◽  
Different Types ◽  
Double Diffusive

When a solute A dissolves into a host fluid containing a reactant B, an A + B → C reaction can influence the convection developing because of unstable density gradients in the gravity field. When A increases density and all three chemical species A, B and C diffuse at the same rate, the reactive case can lead to two different types of density profiles, i.e., a monotonically decreasing one from the interface to the bulk and a non-monotonic profile with a minimum. We study numerically here the nonlinear reactive convective dissolution dynamics in the more general case where the three solutes can diffuse at different rates. We show that differential diffusion can add new dynamic effects like the simultaneous presence of two different convection zones in the host phase when a non-monotonic profile with both a minimum and a maximum develops. Double diffusive instabilities can moreover affect the morphology of the convective fingers. Analysis of the mixing zone, the reaction rate, the total amount of stored A and the dissolution flux further shows that varying the diffusion coefficients of the various species has a quantitative effect on convection.

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