The adjoint linear system on a surface have been studied by many authors. Among these, Reider’s criterion on a smooth surface is very famous. Here we prove a similar criterion on normal surfaces.

We study the damping of internal gravity waves in a stably stratified fluid with constant viscosity in twoand three-dimensional bounded domains. For the linearized Navier-Stokes equations for incompressible flow with no-slip boundary conditions that model this fluid, we prove there are non-oscillatory normal modes with arbitrarily small exponential decay rates. The proof in a twoand three-dimen...

and Applied Analysis 3 satisfy the relation (u, V, w, z) ≥ (u, V, w, z), and for all (u, V) ∈ U × V, satisfy the following inequalities: −Δw +M 1 w ≥ f 1 ( u, V) + M1A (u, V) , x ∈ Ω, −Δz +M 2 z ≥ f 2 ( u, V) + M2B (u, V) , x ∈ Ω, −Δw +M 1 w ≤ f 1 (u, V) + M 1 A (u, V) , x ∈ Ω, −Δz +M 2 z ≤ f 2 (u, V) + M 2 B (u, V) , x ∈ Ω, u ≥ A ∗ (w, z) , V ≥ B ∗ (w, z) , x ∈ Ω, u ≤ A ∗ (w, z) , V ≤ B ∗ (w, ...

Consider the Navier-Stokes equations in a smooth bounded domain Ω ⊂ R and a time interval [0, T ), 0 < T ≤ ∞. It is well-known that there exists at least one global weak solution u with vanishing boundary values u ∣∣ ∂Ω = 0 for any given initial value u0 ∈ Lσ(Ω), external force f = divF , F ∈ L ( 0, T ;L(Ω) ) , and satisfying the strong energy inequality. In this paper we extend this existence ...

This paper considers the nonlinear observer normal forms and their application in an ecological Predator-Prey system. These forms allow for the design of robust observers for Predator-Prey models where full measurement is not available. Thus, from a measured population of one specie (prey or predator), one can estimate the population that is not directly measured.