Difference between revisions of "Quasi-linear equation"
From Encyclopedia of Mathematics
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A partial differential equation (cf. [[Differential equation, partial|Differential equation, partial]]) that is linear with respect to the leading derivatives of the unknown function. For example, the equation | A partial differential equation (cf. [[Differential equation, partial|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 | + | is a second-order quasi-linear equation with respect to the unknown function $u$. |
====Comments==== | ====Comments==== | ||
Latest revision as of 14:48, 10 August 2014
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=18823
Quasi-linear equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-linear_equation&oldid=18823