“parabolic partial differential equation”的概念、定义、翻译、参考文献-科学参考

parabolic partial differential equation

Mathematics

The second order partial differential equation

$A \frac{\partial^{2} f}{\partial x^{2}} + B \frac{\partial^{2} f}{\partial x \partial y} + C \frac{\partial^{2} f}{\partial y^{2}} + D \frac{\partial f}{\partial x} + E \frac{\partial f}{\partial y} + F f + G = 0,$

where A,B,C,D,E,F,G are functions of x and y is parabolic, elliptic, or hyperbolic when B²–4AC is zero, negative, or positive, respectively. So the heat equation is parabolic, Laplace’s equation is elliptic, and the wave equation is hyperbolic.

单词	parabolic partial differential equation
释义	parabolic partial differential equation Mathematics The second order partial differential equation $A \frac{\partial^{2} f}{\partial x^{2}} + B \frac{\partial^{2} f}{\partial x \partial y} + C \frac{\partial^{2} f}{\partial y^{2}} + D \frac{\partial f}{\partial x} + E \frac{\partial f}{\partial y} + F f + G = 0,$ where A,B,C,D,E,F,G are functions of x and y is parabolic, elliptic, or hyperbolic when B²–4AC is zero, negative, or positive, respectively. So the heat equation is parabolic, Laplace’s equation is elliptic, and the wave equation is hyperbolic.
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