Hi, I am new to iMechanica. I am also not sure whether this post is appropriate here or not.

I am doing some instability analysis of heat transfer between two rods having a narrow gap in between them (they might have contacts and separation with time, the gap is a function of temperature T, and T=T(x,t)). I know about the matrix analysis used for stability of a system of ODEs. I am not able to frame my problem (a 1-D transient heat equation with non-linear boundary conditions) properly so that it becomes amenable to the standard matrix method of stability analysis. Does anyone have some references/examples where I can get some help about this (like existence of limit cycles, under which conditions a critical point becomes unstable, etc)? I have the complete numerical solution of the problem and I have seen that for certain input/initial conditions (and parameter values) the solution becomes oscillatory or a steady state solution cannot be obtained.

 Thanks.