Abstract
Using functions convex downward, we describe a class of pseudodifferential systems with entire analytic symbols that contains Éidel’man parabolic systems of partial differential equations with continuous time-dependent coefficients. We prove a theorem on the correct solvability of the Cauchy problem for these systems in the case where initial data are generalized functions. We also establish the principle of localization of a solution of this problem.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 9, pp. 1211–1233, September, 2006.
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Litovchenko, V.A. Cauchy problem for one class of pseudodifferential systems with entire analytic symbols. Ukr Math J 58, 1369–1395 (2006). https://doi.org/10.1007/s11253-006-0138-x
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DOI: https://doi.org/10.1007/s11253-006-0138-x