Eleev, V. A.; Lesev, V. N. On two boundary value problems for mixed type equations with perpendicular lines of type change. (Russian) Zbl 1022.35029 Vladikavkaz. Mat. Zh. 3, No. 4, 9-22 (2001). The authors study boundary value problems for the following partial differential equation of mixed type \[ 0 = \begin{cases} u_{xx} - u_y + f(x,y) &\quad \text{in } \Omega_0 \\ u_{xx} - u_{yy} - \lambda_i^2\operatorname{sign} yu &\quad\text{in } \Omega_i, \end{cases} \] in a complex domain \(\Omega = \Omega_0\cup \Omega_i\). The equation is supplemented by the so-called nonlocal boundary conditions.The purpose of the article is to prove that the boundary value problem admits a unique regular solution. The proof is based on reducing the boundary value problem under consideration to a Volterra integral equation of the second order. Reviewer: V.Grebenev (Novosibirsk) Cited in 1 Document MSC: 35M10 PDEs of mixed type 45D05 Volterra integral equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:parabolic-hyperbolic equation; nonlocal boundary conditions; boundary value problem; existence and uniqueness theorem PDFBibTeX XMLCite \textit{V. A. Eleev} and \textit{V. N. Lesev}, Vladikavkaz. Mat. Zh. 3, No. 4, 9--22 (2001; Zbl 1022.35029) Full Text: EuDML Link