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→Equations of mixed type
If a PDE has coefficients that are not constant, it is possible that it will not belong to any of these categories but rather be of mixed type. A simple but important example is the Euler–Tricomi equation
If a PDE has coefficients that are not constant, it is possible that it will not belong to any of these categories but rather be of mixed type. A simple but important example is the Euler–Tricomi equation
如果偏微分方程的系数不是常数，那么它可能不属于这些类别中的任何一个，而是属于混合类型。一个简单但重要的例子是欧拉-特里科米方程
<math>u_{xx} = xu_{yy},</math>
<math>u_{xx} = xu_{yy},</math>
which is called elliptic-hyperbolic because it is elliptic in the region , hyperbolic in the region , and degenerate parabolic on the line 0}}.
which is called elliptic-hyperbolic because it is elliptic in the region , hyperbolic in the region , and degenerate parabolic on the line 0}}.
它在 {{math|''x'' < 0}} 的区域上是椭圆形，在 {{math|''x'' > 0}} 区域上是双曲形，在 {{math|''x'' {{=}} 0}}这条线上是退化抛物线形，因此称之为椭圆-双曲型。
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fill in: Dirichlet and Neumann boundaries, hyperbolic/parabolic/elliptic separation of variables, Fourier analysis, Green's functions ...-->
fill in: Dirichlet and Neumann boundaries, hyperbolic/parabolic/elliptic separation of variables, Fourier analysis, Green's functions ...-->
填写: Dirichlet 和 Neumann 边界，双曲 / 抛物线 / 椭圆分离变量法，傅立叶变换家族中的关系，Green 函数... --
填写: Dirichlet 和 Neumann 边界，双曲 / 抛物线 / 椭圆分离变量法，傅立叶分析，Green 函数... --
=== Infinite-order PDEs in quantum mechanics ===
=== Infinite-order PDEs in quantum mechanics ===