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Solution of the Tricomi problem for an equation of mixed type with a singular coefficient by means of the spectral method. (English. Russian original) Zbl 1084.35049

Russ. Math. 48, No. 2, 61-68 (2004); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2004, No. 2, 64-71 (2004).
Summary: We consider the equation of S. P. Pulkin \[ u_{xx}+\text{sgn}\,y \cdot u_{yy}+ \frac{2q}{x}u_x=0, \] where \(q\in\mathbb{R}\), in the domain \(D\) which is bounded for \(y<0\) by the characteristics \(AC:x+y=0\), \(A= (0,0)\), \(C=(1/2,-1/2)\) and \(CB:x-y=1\), \(B=(1,0)\); by the segment \(AK\), \(K=(0,k)\), \(k>0\), of the axis \(y\) and by the piecewise smooth curve \(\Gamma\) situated in the first quadrant with the ends at points \(K\) and \(B\).

MSC:

35M10 PDEs of mixed type
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References:

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