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Uniqueness of a solution of the problem \(T\) for an equation of mixed type with conjugation of the normal derivative with the fractional derivative. (English. Russian original) Zbl 1084.35533
Russ. Math. 47, No. 9, 4-7 (2003); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2003, No. 9, 6-9 (2003).
From the text: The following equation is considered: \[ U_{xx}+ \text{sgn}\,y\cdot U_{yy}-\lambda U=0,\;\lambda>0 \] in the domain \(G\) bounded by the smooth curve \(\Gamma\), which lies in the half-plane \(y>0\) and has the ends \(A(0;0)\) and \(B(1;0)\) (the origin of the curve is at the point \(B)\), and segments of the characteristics \(AC:y=-x\), \(BC:y=x-1\), \(C(1/2;-1/2)\).

MSC:
35M10 PDEs of mixed type
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Keywords:
characteristics
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