Existence and a priori bounds for steady stagnation flow toward a stretching cylinder

AbstractWe investigate the nonlinear boundary value problem (BVP) that is derived from a similarity transformation of the Navier–Stokes equations governing fluid flow toward a stretching permeable cylinder. Existence of a solution is proven for all values of the Reynolds number and for both suction and injection, and uniqueness results are obtained in the case of a monotonic solution. A priori bounds on the skin friction coefficient are also obtained. These bounds achieve any desired order of accuracy as the injection parameter tends to negative infinity

Analysis of stagnation point flow of an upper-convected Maxwell fluid

Several recent papers have investigated the two-dimensional stagnation point flow of an upper-convected Maxwell fluid by employing a similarity change of variable to reduce the governing PDEs to a nonlinear third order ODE boundary value problem (BVP). In these previous works, the BVP was studied numerically and several conjectures regarding the existence and behavior of the solutions were made. The purpose of this article is to mathematically verify these conjectures. We prove the existence of a solution to the BVP for all relevant values of the elasticity parameter. We also prove that this solution has monotonically increasing first derivative, thus verifying the conjecture that no ``overshoot'' of the boundary condition occurs. Uniqueness results are presented for a large range of parameter space and bounds on the skin friction coefficient are calculated

A Lotka-Volterra Three-species Food Chain

this paper, we completely characterize the qualitative behavior of a linear threespecies food chain where the dynamics are given by classic (nonlogistic) LotkaVolterra type equations. The Lotka-Volterra equations are typically modified by making the prey equation a logistic (Holling-type [5]) equation to eliminate the possibility of unbounded growth of the prey in the absence of the predator. We study a more basic nonlogistic system that is the direct generalization of the classic Lotka-Volterra equations. Although the model is more simplified, the dynamics of the associated system are quite complicated, as the model exhibits degeneracies that make it an excellent instructional tool whose analysis involves advanced topics such as: trapping regions, nonlinear analysis, invariant sets, Lyapunov-type functions (F and G in what follows), the stable/center manifold theorem, and the Poincar e-Bendixson theorem. Figure 3 Historical plots of hare and lynx pelts collected by the Hudson's Bay Company The model The ecosystem that we wish to model is a linear three-species food chain where the lowest-level prey x is preyed upon by a mid-level species y, which, in turn, is preyed upon by a top level predator z. Examples of such three-species ecosystems include: mouse-snake-owl, vegetation-hare-lynx, and worm-robin-falcon. The model we propose to study is # # # # # # # # # # # # # bxy dy dz gyz, (2) for a, b, c, d, e, f, g > 0, where a, b, c and d are as in the Lotka-Volterra equations and: . e represents the effect of predation on species y by species z, . f represents the natural death rate of the predator z in the absence of prey, . g represents the efficiency and propagation rate of the predator z in the presence of prey. Since populations are nonnegative, we will r..