Limit Behaviour of Solutions to a Class of Equivalued Surface Boundary Value Problems for Parabolic Equations

In this paper, we discuss the limit behaviour of solutions for a class of equivalued surface boundary value problems for parabolic equations. When the equivalued surface boundary overline{Gamma}^varepsilon_1 shrinks to a fixed point on boundary Gamma_1, only homogeneous Neumann boundary conditions or Neumann boundary conditions with Dirac function appear on Gamma_1.