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

Volkodavov, V. F.; Ilyushina, Yu. A.

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