We are considering the problem of state observation for a class of infinite dimensional systems modeled by parabolic type PDEs. The model is subject to parametric uncertainty entering in both the domain equation and the boundary condition. An adaptive boundary observer, providing online estimates of the system state and parameters, is designed using finiteand infinite-dimensional backsteppingli...

We obtain a new result concerning harmonic functions on infinite Cayley graphs X : either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of X . In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. C...

We study the magnetization mL(h, β) for the Ising model on a large but finite lattice square under the minus boundary conditions. Using known large-deviation results evaluating the balance between the competing effects of the minus boundary conditions and the external magnetic field h, we describe the details of its dependence on h as exemplified by the finitesize rounding of the infinite-volum...

In this paper we describe all rotation H-hypersurfaces in Hn × R and use them as barriers to prove existence and characterization of certain vertical H-graphs and to give symmetry and uniqueness results for compact H-hypersurfaces whose boundary is one or two parallel submanifolds in slices. We also describe examples of translation H-hypersurfaces in Hn × R. For n > 2 we obtain a complete embed...

 In the present paper damped vibrations of non-homogeneous infinite rectangular plate of parabolically varying thickness resting on elastic foundation has been studied. Following Lévy approach, the equation of motion of plate of varying thickness in one direction is solved by quintic spline method. The effect of damping, elastic foundation and taperness is discussed with permissible range of pa...

The propagation of shear waves in an anisotropic fluid saturated porous layer over a prestressed semi-infinite homogeneous elastic half-space lying under an elastic homogeneous layer with irregularity present at the interface with rigid boundary has been studied. The rectangular irregularity has been taken in the half-space. The dispersion equation for shear waves is derived by using the pertur...

We establish the existence and stability of multidimensional transonic flows with transonic shocks through an infinite nozzle of arbitrary cross-sections, including a slowly varying de Lavel nozzle. The transonic flow is governed by the inviscid steady potential flow equation with supersonic upstream flow at the entrance, uniform subsonic downstream flow at the infinite exit, and the slip bound...

The problem of plane-wave diffraction on semi-infinite orthorhombic electromagnetic photonic crystals of a general kind is considered. Boundary conditions are obtained in the form of infinite system of equations relating amplitudes of incident wave, eigenmodes excited in the crystal, and scattered spatial harmonics. The generalized Ewald-Oseen extinction principle is formulated on the base of d...

An analysis of heat transfer in the flow of a viscous, in-compressible fluid along an infinite porous plate is presented when the plate is subjected to a transverse sinusoidal suction. The flow field becomes three-dimensional due to this type of suction velocity. Expressions for the flow and temperature fields are obtained by series expansion method. It is found during the course of discussion ...