Detection of Scales of Heterogeneity and Parabolic Homogenization Applying Very Weak Multiscale Convergence

We apply a new version of multiscale convergence named very weak multiscale convergence to find possible frequencies of oscillation in an unknown coefficient of a partial differential equation from its solution. We also use this notion to study homogenization of a certain linear parabolic problem with multiple spatial and temporal scales. 1 Department of engineering and sustainable development, Mid Sweden University, Östersund 83125, Sweden. E-mail address: [email protected] 2 Department of engineering and sustainable development, Mid Sweden University, Östersund 83125, Sweden. E-mail address: [email protected] 3 Department of engineering and sustainable development, Mid Sweden University, Östersund 83125, Sweden. E-mail address: [email protected] 4 Department of engineering and sustainable development, Mid Sweden University, Östersund 83125, Sweden. E-mail address: [email protected] Date: Received: 23 October 2010; Revised: 18 February 2011; Accepted: 12 April 2011. ∗ Corresponding author. 2010 Mathematics Subject Classification. Primary 35B27; Secondary 35K10, 46B50.