Parabolic mixed problems for Petrovskii systems in spaces of generalized smoothness
DOI:
https://doi.org/10.15407/dopovidi2014.10.024Keywords:
mixed problems, Petrovskii systems, spaces of generalized smoothnessAbstract
For some classes of Hilbert spaces of generalized smoothness, we prove a theorem on the wellposedness of parabolic initial-boundary-value problems for Petrovskii systems with zero Cauchy data. The regularity of functions that form these spaces is characterized by a couple of number parameters and a functional parameter. The latter varies regularly at infinity in Karamata's sense. We prove a theorem on a local increase in the regularity of solutions to the problem. We obtain new sufficient conditions, under which the generalized derivatives (of a prescribed order) of the solutions should be continuous.
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