Geodesic
Mixed problem for a~parabolic system on a~plane and boundary integral equations
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 64 (2018) no. 1, pp. 20-36.

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We consider the mixed problem for a one-dimensional (with respect to the spatial variable) second-order parabolic system with Dini-continuous coefficients in a domain with nonsmooth lateral boundaries. Using the method of boundary integral equations, we find a classical solution of this problem. We investigate the smoothness of solution as well. 
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E. A. Baderko; M. F. Cherepova. Mixed problem for a~parabolic system on a~plane and boundary integral equations. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 64 (2018) no. 1, pp. 20-36. http://geodesic.mathdoc.fr/item/CMFD_2018_64_1_a1/

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