THE INITIAL VALUE PROBLEM FOR A COMPOSITE TYPE EQUATION

In connection with the weather forecasting, we consider the initial value problem for the equation of vorticity(∂/∂i+α∂/∂λ)Δz+β(θ)∂z/∂λ=0 where Δ=1/sinθ ∂/∂θ(sinθ∂/∂θ)+1/sin2θ ∂2/∂λ2, with the initial condition z(θ, λ, t)=z0(θ, λ). The required solution z(θ, λ, t) is bounded in the region D: 0