Discussion
True or false: the type of a second-order equation may change from one region to another.
Answer: B
If \( A \), \( B \) and \( C \) depend on \( x \) and \( y \), the discriminant does too, and it may change sign. The Tricomi equation \( y z_{xx} + z_{yy} = 0 \) is elliptic for \( y > 0 \) and hyperbolic for \( y < 0 \), a mixed type that arises physically at transonic speeds. Linearity is not what decides it
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