Mode vector parabolic equation

An adiabatic mode time-dependent parabolic equation

An adiabatic mode time-dependent parabolic equation for the 3D problems of underwater acoustic propagation problem is derived by the multiple-scale method. The Cauchy problem for this equation is considered.

A Nonlinear Parabolic - Sobolev Equation

Let M and I, be (nonlinear) operators in a reflexive Banach space B for which Rg(M + L) = B and j(Mx My) i~(Lx Ly)( > / Mx My / for all 01 > 0 and pairs s, y in D(M) n D(L). Then there is a unique solution of the Cauchy problem (Mu(t))’ + Lu(t) = 0, Mu(O) = v0 . When M and L are realizations of elliptic partial differential operators in space variables, this gives existence and uniqueness of ge...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

Evaluation of Mimo Channel Capacity in Indoor Environments Using Vector Parabolic Equation Method

In this paper, the vector parabolic equation method (VPEM) is used to investigate the Shannon capacity of multiple-input multiple-output (MIMO) communication systems in indoor corridors. This deterministic three-dimensional (3-D) full-wave method is capable to demonstrate the effects of antennas and propagation environment on the channel capacity. The VPEM can model any field depolarization eff...

Stabilization of the Simplest Normal Parabolic Equation

The simplest parabolic equation of normal type with periodic boundary condition is considered, and the problem of stabilization to zero of its solution with arbitrary initial condition by starting control supported in a prescribed subset is investigated. This problem is reduced to one inequality for starting control, and the proof of this inequality is given. Introduction. This paper is devoted...