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Solvability of the oblique derivative problem for second order equations of mixed type with nonsmooth degenerate Curve

J. M. Rassias, Guochun Wen

Abstract


In [1]-[7], the authors posed and discussed the Tricomi problem of second order equations of mixed type, but they only consider some special mixed equations. In [4], the author discussed the uniqueness of solutions of the Tricomi problem for a second order mixed equation with nonsmooth degenerate line. The present article deals with the oblique derivative problem for general second order mixed equations with nonsmooth parabolic degenerate line, which includes the Tricomi problem as a special case, we first give the formulation of the above problem, and then prove the solvability of the problem for the mixed equations with nonsmooth degenerate line. Here we introduce the notation (2.1) below, such that the second order equation of mixed type can be reduced to the mixed complex equation of first order and then we can use the advantage of complex analytic method, otherwise the complex analytic method cannot be used.

Keywords


Oblique derivative problem, mixed equations, nonsmooth degenerate line.

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