Boundary Value Problem for the Gellerstedt Equation in an Unbounded Domain
The Tricomi boundary value problem for the Gellerstedt equation is investigated in
a domain where the elliptic part is the first quadrant of the plane. The unique solvability of the
problem under consideration is established using the method of integral equations. The problem is
equivalently reduced to solving a singular integral equation with a Cauchy kernel. By regularizing
this equation using the Carleman-Vekua method, an explicit solution is obtained.
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