# American Institute of Mathematical Sciences

March  2016, 36(3): 1415-1430. doi: 10.3934/dcds.2016.36.1415

## Effective boundary conditions of the heat equation on a body coated by functionally graded material

 1 Center for Partial Di erential Equations, East China Normal University, Minhang, Shanghai, 200241, China

Received  December 2014 Revised  May 2015 Published  August 2015

We consider the linear heat equation on a bounded domain, which has two components with a thin coating surrounding a body (of metallic nature), subject to the Dirichlet boundary condition. The coating is composed of two layers, the pure ceramic part and the mixed part. The mixed part is considered to be functionally graded material (FGM) that is meant to make a smooth transition from being metallic to being ceramic. The diffusion tensor is isotropic on the body, and allowed to be anisotropic on the coating; and the size of diffusion tensor may differ significantly in these components. We find effective boundary conditions (EBCs) that are approximately satisfied by the solution of the heat equation on the boundary of the body. A concrete example is considered to study the effect of FGM coating. We also provide numerical simulations to verify our theoretical results.
Citation: Huicong Li. Effective boundary conditions of the heat equation on a body coated by functionally graded material. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1415-1430. doi: 10.3934/dcds.2016.36.1415
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##### References:
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