| Abstract: |
| We are interested in the asymptotic behavior of solutions to a heat equation on a body coated by a thin layer. The layer is made of anisotropic material. It was shown previously that as the thickness of the layer shrinks, the effective boundary conditions of the limiting equation contains not only the usual Dirichlet, Neumann and Robin type, but also some exotic type even involving nonlocal type. In this talk, we will discuss how long the effective boundary conditions valid. It is shown that, if both the original equation and the limiting equation converge to zero as time goes to infinity, the life span is infinite; while if they have different long time limit, then the life span will not be infinite but can be characterized by the first eigenvalue of the elliptic operator. |
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