Coupled system of linear parabolic PDEs - MathOverflow most recent 30 from http://mathoverflow.net2013-05-19T02:54:27Zhttp://mathoverflow.net/feeds/question/103297http://www.creativecommons.org/licenses/by-nc/2.5/rdfhttp://mathoverflow.net/questions/103297/coupled-system-of-linear-parabolic-pdesCoupled system of linear parabolic PDEsPinkPanther2012-07-27T11:46:58Z2012-07-27T11:46:58Z
<p>Hi,</p>
<p>Are there any existence results for the coupled system of linear parabolic PDEs:
$$u_t - a_1u_{xx} - a_2u_x - a_3u = f_1$$
$$v_t - a_3u_{xx} - a_4u_x - a_5u - a_6v_{xx} - a_7v_x - a_8v = f_2$$
where the $a_i(x,t)$ are functions with nice properties (eg. continuous). I'm looking for solutions in parabolic Holder space preferably.</p>
<p>I tried Ladyzenskaja but they don't seem to be able to handle this kind of system.</p>
<p>Thank you.</p>