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On some boundary value problems for one mixed equation with discontinuous coefficients in a rectangular domain. (Russian) Zbl 1049.35143
In a domain lying both in a half-plane \(y>0\) and in a half-plane \(y<0\) the authors consider the following equation: \[ 0= \begin{cases} u_{xx}+u_{yy}+\rho_1u+f_0,& y>0, \\ u_{xx}-(-y)^mu_{yy}+\rho_2u_y+\rho_3u,&y<0, \end{cases} \] \(m=0,1\), \(f_{0}\), \(\rho_1\), \(\rho_2\), and \(\rho_3\) are constant numbers. A mixed boundary problem is posed and a regular solution is constructed for this problem. The construction proceeds by the spectral (Fourier) method.
MSC:
35M10 PDEs of mixed type
35R05 PDEs with low regular coefficients and/or low regular data
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