EFFECTIVE BOUNDARY CONDITIONS ARISING FROM THE HEAT EQUATION WITH THREE-DIMENSIONAL INTERIOR INCLUSION

Geng, Xingri1,2

2023-03-01

10.3934/cpaa.2023031

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS   Impact Factor & Quartile

1534-0392

1553-5258

We study the initial boundary value problem for a heat equation in a domain containing a thin layer. The thermal conductivity of the layer is drastically different from that of the bulk of the domain; moreover, the layer is anisotropic and "optimally aligned" in the sense that the normal direction in the layer is always an eigenvector of the thermal tensor. To reveal the effects of the layer, we regard it as a thickless surface on which "effective boundary conditions" (EBCs) are satisfied by the limit of solutions of the initial boundary value problem as the thickness of the layer shrinks to zero. These EBCs are rich in variety and type, including some nonstandard ones such as the Dirichlet-to-Neumann mapping and the fractional Laplacian.

Thin layer a priori estimates asymptotic behavior optimally aligned layers effective boundary conditions

SCI

English

First ; Corresponding

Mathematics

Mathematics, Applied ; Mathematics

WOS:000942895800001

AMER INST MATHEMATICAL SCIENCES-AIMS

MATHEMATICS

Web of Science

1.Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China
2.Natl Univ Singapore, Dept Math, Singapore, Singapore

Geng, Xingri. EFFECTIVE BOUNDARY CONDITIONS ARISING FROM THE HEAT EQUATION WITH THREE-DIMENSIONAL INTERIOR INCLUSION[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS,2023.

Geng, Xingri.(2023).EFFECTIVE BOUNDARY CONDITIONS ARISING FROM THE HEAT EQUATION WITH THREE-DIMENSIONAL INTERIOR INCLUSION.COMMUNICATIONS ON PURE AND APPLIED ANALYSIS.

Geng, Xingri."EFFECTIVE BOUNDARY CONDITIONS ARISING FROM THE HEAT EQUATION WITH THREE-DIMENSIONAL INTERIOR INCLUSION".COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2023).