I have a system of equations for the concentration, $c=c(x,z,t)$. After some simplifying assumptions though, I am left with the following boundary conditions and PDE: $$ c_z=c_{zzz}=0, \qquad \text{on } z=0,h(x,t) $$ $$ c_{zzzz}=0 $$ Can I say that $c$ is independent of $z$? I feel like I should be able to, however, I can't cite any specific reasoning and I'm not quite sure over which intervals to integrate the fourth-order equation.. i.e. over the interval $(0,z), (0,h)$ or $(z,h)$?
2026-03-31 22:49:22.1774997362
What Condition is Necessary to assume a Function is Independent of a Variable
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