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On the question of existence of a solution to the Tricomi problem for one class of systems of mixed-type equations. (Russian, English) Zbl 1003.35098

Sib. Mat. Zh. 43, No. 3, 710-727 (2002); translation in Sib. Math. J. 43, No. 3, 575-590 (2002).
The authors apply the Schwartz alternating method to study the Tricomi problem for the system \[ K(y)u_{ixx}+u_{iyy}+A_i(x,y)u_{ix}+B_i(x,y)u_{iy} +\sum_{k=1}^nC_{ik}(x,y)u_k=F_i(x,y), \] where \(K(y)\), \(A_i(x,y)\), \(B_i(x,y)\), \(C_{ik}(x,y)\), and \(F_i(x,y)\), \(i,k=1,\dots,n\), are given functions, and \(yK(y)>0\) for \(y\neq 0\). The authors prove a maximum principle and establish uniqueness of a weak solution in the domain bounded in the elliptic part by a curve approaching the axis \(y=0\) arbitrarily.

MSC:

35M10 PDEs of mixed type
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