Category:Quasilinear equations: Difference between revisions
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<center> [[Mean curvature flow]] </center> | <center> [[Mean curvature flow]] </center> | ||
\[ u_t = \mbox{div} \left ( u \nabla \mathcal{K} u ,\;\; \mathcal{K} u = u * |x|^{n+\alpha} | \[ u_t = \mbox{div} \left ( u \nabla \mathcal{K} u\right ),\;\;\; \mathcal{K} u = u * |x|^{n+\alpha} \] | ||
<center> [[Nonlocal porous medium equation]] </center> | <center> [[Nonlocal porous medium equation]] </center> | ||
Revision as of 16:22, 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)
\[u_t-\mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \]
\[ u_t = \mbox{div} \left ( u \nabla \mathcal{K} u\right ),\;\;\; \mathcal{K} u = u * |x|^{n+\alpha} \]
Equations which are not quasilinear are called Fully nonlinear equations, which include for instance Monge Ampére and Fully nonlinear integro-differential 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.