# Quasi-linear equation

From Encyclopedia of Mathematics

A partial differential equation (cf. Differential equation, partial) that is linear with respect to the leading derivatives of the unknown function. For example, the equation

$$\left(\frac{\partial u}{\partial x}\right)^2\frac{\partial^2u}{\partial x^2}+\frac{\partial u}{\partial y}\frac{\partial^2u}{\partial y^2}+u^2=0$$

is a second-order quasi-linear equation with respect to the unknown function $u$.

#### Comments

#### References

[a1] | H.M. Luberstein, "Theory of partial differential equations" , Acad. Press (1972) pp. 10; 12; 27 |

[a2] | G.F. Carrier, C.E. Pearson, "Partial differential equations" , Acad. Press (1976) pp. Sect. 6.3; 89; 252 |

**How to Cite This Entry:**

Quasi-linear equation.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Quasi-linear_equation&oldid=32818