Electronic Journal of Differential Equations, Vol. 2008(2008), No. 31, pp. 1-15. Title: Parabolic boundary-value problems with equivalued surface on the domain with a thin layer Authors: Meihua Du (Dalian Univ. of Technology, Dalian, China) Fengquan Li (Dalian Univ. of Technology, Dalian, China) Abstract: We study the existence, uniqueness and limit behavior of solutions to parabolic boundary-value problems with equivalued surface on a domain with a thin layer. Submitted August 29, 2007. Published March 06, 2008. Math Subject Classifications: 35A05, 35B40, 35K20. Key Words: Limit behavior of solutions; existence; uniqueness; equivalued surface; equivalued interface.