Category:Quasilinear equations: Difference between revisions

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\[ \mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \]
\[ \mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \]
\[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \]  
\[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \]  
\[ (-\Delta)^{s} u +H(x,u,\nabla u)=0 (2s>1) \]
\[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0 (2s>1) \]


In particular, note that all [[Semilinear equations]] are automatically quasilinear.
In particular, note that all [[Semilinear equations]] are automatically quasilinear.

Revision as of 17:12, 3 June 2011

A quasilinear equation is one that is linear in all but the terms involving the highest order derivatives (whether they are of fractional order or not). For instance, the following equations are all quasilinear

\[ \mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \] \[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \] \[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0 (2s>1) \]

In particular, note that all Semilinear equations are automatically quasilinear.

Pages in category "Quasilinear equations"

The following 2 pages are in this category, out of 2 total.