Multipoint boundary value problem with inequalities for parabolic equations with degeneracy

Pukalskyi Ivan; Yashan Bohdan Olehovych

doi:https://doi.org/10.31861/bmj2018.03.118

Pukalskyi Ivan ¹ , Yashan Bohdan Olehovych ¹

¹ Department of Differential Equations, Yuriy Fedkovych Chernivtsi National University, Chernivtsi, 58000, Ukraine

DOI: https://doi.org/10.31861/bmj2018.03.118

Keywords: boundary condition, solution of the problem, interpolation inequalities, norm

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Abstract

The algorithm for finding solution a multipoint in time variable of a one-sided boundary value problem for a second order parabolic equation is offered. The coefficients of the equation and the boundary conditions are degenerate and have power singularities in time and space variables of arbitrary order on a certain set of points. Existence and uniqueness of the solution of the problem in Hölder spaces with power weight are established. The order of power degree depends on the magnitude of features of the coefficients of the equation and boundary conditions. In the allocated Hölder spaces estimations of derivatives of solution of the problem are established.

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ACS Style: Pukalskyi, I.; Yashan, B.O. Multipoint boundary value problem with inequalities for parabolic equations with degeneracy. Bukovinian Mathematical Journal. 2019, 6 https://doi.org/https://doi.org/10.31861/bmj2018.03.118
AMA Style: Pukalskyi I, Yashan BO. Multipoint boundary value problem with inequalities for parabolic equations with degeneracy. Bukovinian Mathematical Journal. 2019; 6(3-4). https://doi.org/https://doi.org/10.31861/bmj2018.03.118
Chicago/Turabian Style: Ivan Pukalskyi, Bohdan Olehovych Yashan. 2019. "Multipoint boundary value problem with inequalities for parabolic equations with degeneracy". Bukovinian Mathematical Journal. 6 no. 3-4. https://doi.org/https://doi.org/10.31861/bmj2018.03.118

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