一个与中长期预报有关的复合型方程的定解问题
THE INITIAL VALUE PROBLEM FOR A COMPOSITE TYPE EQUATION
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摘要: 本文研究了涡度方程(∂/∂i+α∂/∂λ)Δz+β(θ)∂z/∂λ=0的始值问题,其中Δ=1/sinθ ∂/∂θ(sinθ∂/∂θ)+1/sin2θ ∂2/∂λ2方法是先用特征线法问题将化为积分方程,然后再对积分方程施行逐次迫近,从而证明了问题的适定性,并提供了求解的步骤.这方法可推广到更一般的方程.Abstract: 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
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