一类线性偏微分方程的相似解

Approximate Solution of a Linear Partial Differential Equation

研究方程((e)u)/((e)t)=xpΔu, (x,t)∈R2×(0,+∞)的具有形式u(x,t)=(t+1)λw(ξ)的相似解的存在惟一性及渐近性质,这里0≤p<2,λ∈R,ξ=(xβ)/((t+1)α),α>0,β=α(2-p).

The paper studies the uniqueness of existence and asymptotu property of the equationut=x^pΔu,(x,t)∈R^2×(0,+∞) which has approximate solution u(x,t)=(t+1)~λw(ξ), where 0≤p<2,λ∈R,ξ=x~β(t+1)~α,α>and β=α(2-p).