Homogenization of Parabolic Equations in Domains of Degenerating Measure

We consider the Neumann boundary value problem for linear and nonlinear PDE of parabolic type in strongly perforated domains z ( l ) of asymptotically degenerating measure, i.e. meas z ( l ) M 0 as l M 0. Here l stands for the parameter that characterizes the scale of the microstructure. It is shown that the homogenization of this problem leads to the Neumann boundary value problem of the parabolic type with the coefficients obtained by some local characteristics of the domain z ( l ) .

Keywords:

• Homogenization
• Parabolic Equations
• Strongly Perforated Domains
• Domains Of Asymptotically Degenerating Measure
• Lattice-like Structures