Timeline for Coupled system of linear parabolic PDEs
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 28, 2012 at 1:03 | comment | added | Hans Engler | I don't think you'll get good results if the $a_i$ are merely continuous, since in that case there may not be a good maximal regularity theory. But if all coefficients and the $f_i$ are in $C^{\alpha,\alpha/2}$ in the sense of Ladyzhenskaya, then the mapping $M: f_1 \mapsto a_3u_{xx} + a_4 u_x + a_5 u$ is linear and bounded and therefore you are just solving a linear equation for $v$. | |
| Jul 27, 2012 at 14:17 | comment | added | PinkPanther | I am interested in this as I want to apply an inverse function theorem argument for existence of a nonlinear system. | |
| Jul 27, 2012 at 14:17 | comment | added | PinkPanther | @Deane it's definitely not homework. | |
| Jul 27, 2012 at 13:24 | comment | added | Deane Yang | Your question makes this sound like homework. | |
| Jul 27, 2012 at 12:48 | comment | added | PinkPanther | Can I not solve for $u$ first, then solve for $v$? | |
| Jul 27, 2012 at 11:46 | history | asked | PinkPanther | CC BY-SA 3.0 |