In this paper we study the effects of small viscosity term and the far-field boundary conditions for systems of convection-diffusion equations in the zero viscosity limit. The far-field boundary conditions are classified and the corresponding solution structures are analyzed. It is confirmed that the Neumann type of far-field boundary condition is preferred. On the other hand, we also identify ...

The following von Neumann-Wigner type result is proved: The set of potentials a: T —► R (r Ç ZN), with the property that the corresponding discrete Schrödinger equation A¿ + a has multiple eigenvalues when considered with certain boundary conditions, is an algebraic set of codimension> 2 within Rr.

We consider an inhomogeneous thermoelastic system with second sound in one space dimension where the coe cients are spaceand time-dependent. For Dirichlet-Neumann type boundary conditions the global existence of smooth solutions is proved by using the theory of Kato. Then the asymptotic behavior of the solutions is discussed.

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove ...

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we show that, as the competition rate grows indefinitely, the system reaches a state of coexistence of all the species in spatial segregation. Furthermore, the limit configuration is a local minimizer for th...

The null exact controllability of Predator-prey model with homogeneous Neumann boundary conditions is studied.A carleman type estimate for adjoint linearized system is firstly established.Then we get the controllability of the linearized system. Finally, null exact controlla-bility for the nonlinear problem is obtained using the Kakutani's fixed point theorem.

This paper discusses a predator-prey system with Holling-(n + 1) functional response and the fractional type nonlinear diffusion term in a bounded domain under homogeneous Neumann boundary condition.The existence and nonexistence results concerning nonconstant positive steady states of the system were obtained. In particular, we prove that the positive constant solution (?̃?, Ṽ) is asymptoticall...

We study the solvability of the equation x′′ = f(t,x,x′) subject to Dirichlet, Neumann, periodic, and antiperiodic boundary conditions. Under the assumption that f can be suitably decomposed, we prove approximation solvability results for the above equation by applying the abstract continuation type theorem of Petryshyn on A-proper mappings.