Abstract
We consider the first initial–boundary value problem for a second-order Petrovskii parabolic homogeneous system with constant coefficients in a bounded domain \(\Omega \) on the plane with curvilinear lateral boundaries nonsmooth at \(t=0 \). The existence of a solution of this problem in the class \( C^{2,1}_{x,t}(\overline {\Omega })\) is proved by the method of boundary integral equations.
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ACKNOWLEDGMENTS
The author expresses his deep gratitude to Prof. E.A. Baderko for setting the problem and for constant attention to the work.
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Translated by V. Potapchouck
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Fedorov, K.D. On the First Initial–Boundary Value Problem for a Model Parabolic System in a Domain with Curvilinear Lateral Boundaries. Diff Equat 57, 1598–1609 (2021). https://doi.org/10.1134/S0012266121120065
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DOI: https://doi.org/10.1134/S0012266121120065