most recent 30 from http://mathoverflow.net 2013-05-19T03:00:36Z http://mathoverflow.net/feeds/question/40037 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/40037/inconsistency-in-definition-of-characteristics-for-a-linear-pde-folland-versus-f Dorian 2010-09-26T16:54:17Z 2010-09-26T16:54:17Z

<p>There seems to be a major inconsistency (perhaps due to my lack of understanding) between what Folland calls a "characteristic" and what I had previously thought was a characteristic.</p> <p>For example, Folland says that the characteristics of the equation $\partial_x u = 0$ are <code>$\{ \xi : \xi_1 = 0\}$</code> (in $\mathbb{R}^2$). This confuses me to no end since I thought the characteristic hypersurface was the $x_1$ axis here? According to this definition it's the orthogonal compliment to this. The same issue arises with the heat operator $L=u_t-u_{xx}$ where he says the characteristics are <code>$\{\xi \neq 0 : \xi_x = 0\}$</code>. Aren't the characteristics $t=$ cosntant which are orthogonal to these?</p> <p>Sorry if this question is elementary but it's given me a real headache and I'm not sure what it is I'm missing here.</p>