Specialization: 011200 Physics
Program: 07 Methods and problems of mathematical and computational physics
Head of the program: prof. T. A. Suslina
Department of higher mathematics and mathematical physics
Scientific adviser: prof. T. A. Suslina
Reviewer: prof. S. A. Nazarov

Homogenization of the Cauchy problem for parabolic systems                          with periodic coefficients
	Yu. M. Meshkova

In the space L2(Rd;Cn), a class of matrix second order differential operators Bε with rapidly oscillating coefficients (depending on x/ε) is considered. For a fixed s>0 and small ε>0, approximation is found for the operator exp(-Bεs) in the (L2→L2)- and (L2→H1)-norm with an error term of order of ε. The results are applied to homogenization of solutions of the parabolic Cauchy problem.

	The list of publications
	1. Meshkova Yu. M., Homogenization of the Cauchy problem for parabolic equation with periodic coefficients // The Twenty Third Crimean Autumn Mathematical School (KROMSH-2012), book of abstracts. – Simferopol, 2012. – p. 43. (In Russian.)
	2. Meshkova Y. M., Homogenization of the Cauchy problem for a parabolic equation with periodic coefficients // International Student Conference “Science and progress”, conference abstracts. – Saint Petersburg: SOLO, 2012. – p. 146.
	3. Meshkova Y. M., Homogenization in the Sobolev class H1(Rd) of the Cauchy problem for a parabolic equation with rapidly oscillating coefficients // International Conference “Days on Diffraction 2013”, abstracts. – Saint Petersburg, 2013. – p. 63-64.
	4. Meshkova Yu. M., Homogenization of parabolic systems with periodic coefficients with the correction term taken into account // Crimea International Mathematical Conference (CIMC-2013), book of abstracts, vol. 2. – Simferopol, 2013. – p. 49. (In Russian.)
	5. Meshkova Yu. M., Homogenization of the Cauchy problem for parabolic systems with periodic coefficients // Algebra i Analiz, vol. 25 (2013), issue 6. – p. 125-177. (In Russian); English. transl., St. Petersburg Math. J., vol. 25 (2014), issue 6, to appear.