In the case where initial data are generalized functions of the Gevrey-distribution type for which the classical notion of equality of two functions on a set is well defined, we establish the principle of local strengthening of the convergence of a solution of the Cauchy problem to its limit value as t → +0 for one class of degenerate parabolic equations of the Kolmogorov type with \( \overrightarrow {2b} \)-parabolic part whose coefficients are continuous functions that depend only on t.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 11, pp. 1473–1489, November, 2010.
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Litovchenko, V.A., Strybko, O.V. Principle of localization of solutions of the Cauchy problem for one class of degenerate parabolic equations of Kolmogorov type. Ukr Math J 62, 1707–1728 (2011). https://doi.org/10.1007/s11253-011-0462-7
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DOI: https://doi.org/10.1007/s11253-011-0462-7