Continuous dependence for the Brinkman–Forchheimer fluid interfacing with a Darcy fluid in a bounded domain

Structural stability for the Boussinesq equations interfacing with Darcy equations in a bounded domain

“…We want to know whether a slight change in the coefficients in the equations or boundary data, or even the equation itself, will lead to drastic changes in the solution. For a review of the nature of the structural stability, refer [13][14][15], Scott [16], Scott and Straughan [17], Payne et al [18][19][20][21] and some related papers [22][23][24]. The previous publications of structural stability usually study one fluid in a bounded domain.…”

Convergence Results on the Boundary Conditions for 2D Large-Scale Primitive Equations in Oceanic Dynamics

“…Since some inevitable errors will appear in reality, the study of continuous dependence or convergence results becomes more and more significant. ere have been many papers in the literature to study the continuous dependence or convergence for varieties of equations (e.g., Brinkman, Darcy, and Forchheimer equations) (see [15][16][17][18][19][20][21]). For some type of primitive equations, one can see [22,23].…”

Continuous dependence on boundary and Soret coefficients in double diffusive bidispersive convection

“…In many ways, continuous dependence of the solution in changes in the differential equations or boundary conditions is as important as continuous dependence upon the initial data or stability. In fact, continuous dependence on the model occupies much recent research, see for example, Celik and Hoang, 38 Ciarletta et al, 39 Franchi et al, 18 Gentile and Straughan, 21 Harfash, 40 Hoang and Thinh, 41 Kalantarova and Ugurlu, 42 Li et al, 43 Liu, 44 Liu and Xiao, 45 Liu et al, 46 Scott, 47 Varsakelis and Papalexandris, 48 and Wang and Su 49 …”