Asymptotics of heat conduction in a bar capped with a thin, poorly conductive skin
L. E. Bobisud, George C. Hsiao · Applicable Analysis · 1982
AMS (MOS) 35K05, 35B20, 80A20 We consider a heat-conducting bar in the region 0>x>1 capped with a poorly conductive material in the region -∊>x>0 in the limit as the conductivity σ2 and the thickness ∊ tend to zero. Boundary conditions at x=1 and x=-ε are of Dirichlet type. If , then the thin skin behaves in the limit like an insulator; if it behaves like a perfect conductor. The case of equaling a constant k is much more interesting, and is the only case pursued in detail. For in this case the solution in the bar approaches the solution of a degenerate boundary value problem that has a boundary condition of the third type at the end i:x=0. First-order correction terms are also obtained; these terms again satisfy a boundary condition of third kind at the capped end.