Non-local in time multipoint problem for $2b$-parabolic equations with degeneration

I. D. Pukal’skii; B. O. Yashan

doi:10.30970/ms.64.2.144-152

I. D. Pukal’skii Yury Fedkovich Chernivtsi National University, Chernivtsi, Ukraine
B. O. Yashan Yury Fedkovich Chernivtsi National University, Chernivtsi, Ukraine

DOI: https://doi.org/10.30970/ms.64.2.144-152

Keywords: 2b-parabolic equations, degeneration, Arzela–Ascoli theorem, multipoint problem, apriori estimates, power singularities

Abstract

Problems for partial differential equations are arise in various branches of mathematics, mechanics, engineering, economics, ecology, and other sciences. Equations with degeneracy in spatial variables by an operator, in particular the singular Bessel operator, describe some diffusion processes, thermal mass transfer phenomena, radial oscillations are found in crystallography and other applied problems.

The conditions for the unique solvability of a nonlocal multipoint problem in time for $2b$-parabolic equations with degeneration are investigated. The coefficients of the parabolic equations admit power singularities and degeneration of arbitrary order in any variables on a certain set of points. Estimates of the solutions of the problem in H\"{o}lder spaces with power weight are established. The order of the power weight is determined by the magnitudes of the power singularities and degenerations of the coefficients of the $2b$-parabolic equations.

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