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| =Sample 1=
| | 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) |
| <span style="margin:3px; background:#cedff2; font-size:120%; font-weight:bold; border:1px solid #a3b0bf; text-align:center; color:#000; padding:0.2em 0.4em;"> This is fancy. </span>
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| | \[ \mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \] |
| | \[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \] |
| | \[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0\;\; (2s>1) \] |
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| | Equations which are not quasilinear are called [[Fully nonlinear]]. Note that all [[Semilinear equations]] are automatically quasilinear. |
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| {{infobox|
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| <math>\int_0^\infty e^{-x} dx</math> This works fine
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| {{note|text=$1+1=2$ If I give a name or number to the parameter, math comes out just fine.
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| However, it bothers me that I cannot put two separate paragraphs inside a note.
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| I'm not sure why, but putting a line with a colon in between seems to separate paragraphs for templates.
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| {{note|text=You mean
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| {{sketchproof| text=How do you create new templates? One way is to declare it in the code itself, which after saving the page will create a placeholder for the template.
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| ==References==
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| *{{Citation | last1=Gilbarg | first1=David | last2=Trudinger | first2=Neil S. | author2-link=Neil Trudinger | title=Elliptic partial differential equations of second order | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | isbn=978-3-540-41160-4 | year=2001}}
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| =Sample 2: Inline references=
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| <!-- If we wanted to be more fancy - this will not render properly until Maorung installs the Cite extension -->
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| This is a citation.<ref name="GT"/> And also this ones. <ref name="MR3048593" /> <ref name="evans" />
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| =Sample Picture=
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| ==References==
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| <ref name="GT">{{Citation | last1=Gilbarg | first1=David | last2=Trudinger | first2=Neil S. | author2-link=Neil Trudinger | title=Elliptic partial differential equations of second order | publisher=[[Springer-Verlag]] | location=Berlin, New York | edition=2nd | isbn=978-3-540-41160-4 | year=2001}}</ref>
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| <ref name="MR3048593">{{Citation | last1=Yang | first1= Ray | title=Optimal Regularity and Nondegeneracy of a Free Boundary Problem Related to the Fractional Laplacian | url=http://dx.doi.org/10.1007/s00205-013-0619-7 | journal=Arch. Ration. Mech. Anal. | issn=0003-9527 | year=2013 | volume=208 | pages=693--723 | doi=10.1007/s00205-013-0619-7}}</ref>
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| <ref name="evans">{{Citation | last1=Evans | first1= Lawrence C. | title=Partial differential equations | publisher=American Mathematical Society | year=1998 | volume=19 | pages=xviii+662}}</ref>
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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)
\[ \mbox{div} \left ( \frac{\nabla u}{\sqrt{1+|\nabla u|^2}}\right ) = 0 \]
\[ u_t = \mbox{div} \left ( u^p \nabla u\right ) \]
\[ u_t+(-\Delta)^{s} u +H(x,t,u,\nabla u)=0\;\; (2s>1) \]
Equations which are not quasilinear are called Fully nonlinear. Note that all Semilinear equations are automatically quasilinear.