Category:Quasilinear equations: Difference between revisions
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\[u_t-\mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \] | \[u_t-\mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \] | ||
\[ \mbox{ [[Semilinear equations]]}\] | |||
\[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \] | \[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \] | ||
\[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0\;\; (2s>1) \] | \[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0\;\; (2s>1) \] | ||
Equations which are not quasilinear are called [[Fully nonlinear]]. Note that all [[Semilinear equations]] are automatically quasilinear. | Equations which are not quasilinear are called [[Fully nonlinear equations]]. Note that all [[Semilinear equations]] are automatically quasilinear. | ||
Revision as of 16:16, 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 (and not semilinear)
\[u_t-\mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \]
\[ \mbox{ [[Semilinear equations]]}\]
\[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \] \[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0\;\; (2s>1) \]
Equations which are not quasilinear are called Fully nonlinear equations. 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.