HOMOGENIZATION OF THE CAUCHY PROBLEM FOR PARABOLIC SYSTEMS WITH PERIODIC COEFFICIENTS

作者：Meshkova Yu M^*

来源：St Petersburg Mathematical Journal, 2014, 25(6): 981-1019.

DOI：10.1090/S1061-0022-2014-01326-X

• Parabolic equation
• Cauchy problem
• homogenization
• corrector

In L-2(R-d; C-n), a class of matrix second order differential operators B-epsilon with rapidly oscillating coefficients (depending on x/epsilon) is considered. For a fixed s %26gt; 0 and small epsilon %26gt; 0, approximation is found for the operator exp(-B(epsilon)s) in the (L-2 -%26gt; L-2)- and (L-2 -%26gt; H-1)-norm with an error term of order of epsilon. The results are applied to homogenization of solutions of the parabolic Cauchy problem.

• 出版日期2014-12