一类一阶和二阶Fuchs型拟微分算子Cauchy问题K-flat解的唯一性

UNIQUENESS OF K-FLAT SOLUTION FOR THE CAUCHY PROBLEM OF 1-ORDER AND 2-ORDER FUCHS TYPE PSEUDODIFFERENTIAL OPERATORS

考虑下面的一类一阶和二阶Fuchs型拟微分算子的Cauchy问题其中ε_1,ε_2=0,1,P_1∈OPS_((t,0))~1(Ω_δ),A∈OPS_((t,x))~1(M),P_2∈OPS_((t))~2(Ω_δ),P_1,A,P_2均具正算符。对L_1,L_2建立相应的Carleman型估计,从而得到K-flat解的唯一性。

This paper presents the definition of K-flat solution and results on the uniqueness forthe cauchy problem of 1-order and 2-order Fuchs type pseudodifferential operators. Weconsider following Fuchs type pseudodifferential operators:L_1=t(?)_t,+α(x)+t^(ε_1)P_1(t,0,xD_x)+t^(ε_2)∧(,x,0,D_0)L_2=t^2(?)_t^2+α(x)t(?)_t+β(x)+P_2(t,x,D_x)where ε_1, ε_2=0, 1, P_1∈OPS_(t,0)~1(Ω_δ), ∧∈OPS_(t,x)~1(M), P_2∈OPS_(t)~2(Ω_δ).The symbol of P_1, ∧, P_2 is positive.