Cauchy problem for one class of pseudodifferential systems with entire analytic symbols
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.
English version (Springer): Ukrainian Mathematical Journal 58 (2006), no. 9, pp 1369-1395.
Citation Example: Litovchenko V. A. Cauchy problem for one class of pseudodifferential systems with entire analytic symbols // Ukr. Mat. Zh. - 2006. - 58, № 9. - pp. 1211–1233.
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