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Linearity

A PDE is called linear, if for two solutions $u,v$ the function $\lambda u+\mu v$ is also a solution.
$\displaystyle \Delta u$ $\textstyle \equiv$ $\displaystyle 0\hspace{1cm}\mbox{is linear}$  
$\displaystyle u_x^2+u_y$ $\textstyle =$ $\displaystyle 0\hspace{1cm}\mbox{is not linear}$  

because $u=x-y$ is a solution, but $u=2x-2y$ is not a solution.


Heiko Enderling 2003-11-13