Semilinear: Difference between revisions
From DispersiveWiki
Jump to navigationJump to search
No edit summary |
m (Clarified antecedent of "these equations") |
||
| Line 8: | Line 8: | ||
<center><math>L u = F(u, Du, \ldots, D^k u)</math></center> | <center><math>L u = F(u, Du, \ldots, D^k u)</math></center> | ||
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 | 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 | ||
''k'' strictly less than the order of ''L''. | ''k'' strictly less than the order of ''L''. Semilinear-with-derivatives equations are more nonlinear than semilinear equations, but are less nonlinear than [[quasilinear]] or [[fully nonlinear]] equations. | ||
[[Category:concept]] | [[Category:concept]] | ||
Latest revision as of 15:41, 12 December 2007
A semilinear equation is a PDE of the form
where L is a linear operator and F is a nonlinear operator which does not involve any derivatives of u.
A semilinear-with-derivatives equation is a PDE of the form
where L is a linear operator, F is a nonlinear function of the first few derivatives , with k strictly less than the order of L. Semilinear-with-derivatives equations are more nonlinear than semilinear equations, but are less nonlinear than quasilinear or fully nonlinear equations.
