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| 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)
| | #redirect [[comparison principle]] |
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| \[u_t-\mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \]
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| \[ \mbox{ [[Semilinear equations]]}\]
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| \[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \]
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| \[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0\;\; (2s>1) \]
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| Equations which are not quasilinear are called [[Fully nonlinear equations]]. Note that all [[Semilinear equations]] are automatically quasilinear.
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Latest revision as of 20:40, 24 April 2012
Pages in category "Quasilinear equations"
The following 2 pages are in this category, out of 2 total.