We study the smoothness in the Dini space of a vector parabolic volume potential whose density can be unbounded near the parabolic boundary of the domain. We establish the solvability of initial-boundary value problems for inhomogeneous parabolic systems with Dini continuous coefficients in a semibounded domain on the plane. We prove estimates for solutions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. F. Cherepova, “On some properties of the parabolic potential of bulk masses. I,” Differ. Equations 35, No. 12, 1726-1732 (1999).
L. I. Kamynin, “On solution of the fundamental boundary value problems for a one-dimensional parabolic equation of second order by the method of potentials,” Sib. Math. J. 15, No. 4, 573–592 (1974).
E. A. Baderko, “Potential for 2p-parabolic equations,” Differ. Equations 19, No. 1, 6–14 (1983).
I. V. Zhenyakova and M. F. Cherepova, “Regularity of solution to the Cauchy problem for parabolic equation in the Dini space,” J. Math. Sci. 259, No. 2, 172–186 (2021).
E. A. Baderko and M. F. Cherepova, “Dirichlet problem for parabolic systems with Dini continuous coefficients on the plane,” Dokl. Math. 96, No. 2, 423–426 (2017).
E. A. Baderko and M. F. Cherepova, “Dirichlet problem for parabolic systems with Dini continuous coefficients,” Appl. Anal. 100, No. 13, 2900–2910 (2021).
E. A. Baderko and M. F. Cherepova, “The first boundary value problem for parabolic systems in plane domains with nonsmooth lateral boundaries,” Dokl. Math. 90, No. 2, 573–575 (2014).
E. A. Baderko and M. F. Cherepova, “Simple layer potential and the first boundary value problem for a parabolic system on the plane,” Differ. Equ. 52, No. 2, 197–209 (2016).
L. I. Kamynin, “On smoothness of thermal potentials in Dini–Hölder space,” Sib. Math. J. 11, No. 5, 757–776 (1970).
E. A. Baderko and S. I. Sakharov, “Uniqueness of solutions of initial-boundary value problems for parabolic systems with Dini continuous coefficients in domains on the plane,” Dokl. Math. 105, No. 2, 71–74 (2022).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhenyakova, I.V., Cherepova, M.F. Volume Potential and Initial–Boundary Value Problems for Parabolic Systems with Dini Continuous Coefficients in the Plane. J Math Sci 274, 567–582 (2023). https://doi.org/10.1007/s10958-023-06621-9
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-023-06621-9