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Tricomi equation : ウィキペディア英語版
Euler–Tricomi equation
In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named for Leonhard Euler and Francesco Giacomo Tricomi.
:
u_=xu_. \,

It is hyperbolic in the half plane ''x'' > 0, parabolic at ''x'' = 0 and elliptic in the half plane ''x'' < 0.
Its characteristics are
: x\,dx^2=dy^2, \,
which have the integral
: y\pm\fracx^=C,
where ''C'' is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line ''x'' = 0, the curves lying on the right hand side of the ''y''-axis.
==Particular solutions==

Particular solutions to the Euler–Tricomi equations include
* u=Axy + Bx + Cy + D, \,
* u=A(3y^2+x^3)+B(y^3+x^3y)+C(6xy^2+x^4), \,
where ''A'', ''B'', ''C'', ''D'' are arbitrary constants.
The Euler–Tricomi equation is a limiting form of Chaplygin's equation.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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