We introduce multi-weighted parabolic operators and show that the class of such operators is closed under compositions. We prove the solvability of initial-value problems for multi-weighted parabolic equations in anisotropic Sobolev–Slobodetsky spaces and also for multi-weighted parabolic systems that are simultaneously multi-order systems relative to the spatial variables. Bibliography: 15 titles.
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Translated from Problemy Matematicheskogo Analiza 71, June 2013, pp. 109–122.
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Kozhevnikov, A. Multi–Weighted Parabolic Equations and Systems. J Math Sci 193, 267–282 (2013). https://doi.org/10.1007/s10958-013-1452-0
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DOI: https://doi.org/10.1007/s10958-013-1452-0