https://dispersivewiki.org/DispersiveWiki/index.php?title=Semilinear&feed=atom&action=historySemilinear - Revision history2024-03-28T14:33:54ZRevision history for this page on the wikiMediaWiki 1.39.3https://dispersivewiki.org/DispersiveWiki/index.php?title=Semilinear&diff=5254&oldid=prevPblue: Clarified antecedent of "these equations"2007-12-12T15:41:44Z<p>Clarified antecedent of "these equations"</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 15:41, 12 December 2007</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center><math>L u = F(u, Du, \ldots, D^k u)</math></center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center><math>L u = F(u, Du, \ldots, D^k u)</math></center></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where ''L'' is a linear operator, ''F'' is a nonlinear function of the first few derivatives <math>u, Du, \ldots, D^k u</math>, with</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>where ''L'' is a linear operator, ''F'' is a nonlinear function of the first few derivatives <math>u, Du, \ldots, D^k u</math>, with</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>''k'' strictly less than the order of ''L''. <del style="font-weight: bold; text-decoration: none;">These </del>equations are more nonlinear than semilinear equations, but are less nonlinear than [[quasilinear]] or [[fully nonlinear]] equations.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>''k'' strictly less than the order of ''L''. <ins style="font-weight: bold; text-decoration: none;">Semilinear-with-derivatives </ins>equations are more nonlinear than semilinear equations, but are less nonlinear than [[quasilinear]] or [[fully nonlinear]] equations.</div></td></tr>
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</table>Pbluehttps://dispersivewiki.org/DispersiveWiki/index.php?title=Semilinear&diff=3377&oldid=prevTao at 00:40, 8 August 20062006-08-08T00:40:06Z<p></p>
<p><b>New page</b></p><div>{{stub}}<br />
<br />
A '''semilinear''' equation is a PDE of the form<br />
<center><math>L u = F(u)</math></center><br />
where ''L'' is a linear operator and ''F'' is a nonlinear operator which does not involve any derivatives of ''u''.<br />
<br />
A '''semilinear-with-derivatives''' equation is a PDE of the form<br />
<center><math>L u = F(u, Du, \ldots, D^k u)</math></center><br />
where ''L'' is a linear operator, ''F'' is a nonlinear function of the first few derivatives <math>u, Du, \ldots, D^k u</math>, with<br />
''k'' strictly less than the order of ''L''. These equations are more nonlinear than semilinear equations, but are less nonlinear than [[quasilinear]] or [[fully nonlinear]] equations.<br />
<br />
[[Category:concept]]</div>Tao