Dirichlet problem for parabolic systems with Dini continuous coefficients. Issue 13 (3rd October 2021)

• Record Type: Journal Article
• Authors: Baderko, E. A.; Cherepova, M. F.
• Is Part Of: Applicable analysis. Volume 100:Issue 13(2021)
• Page Start: 2900
• Page End: 2910
• Publication Date: 2021-10-03
• Subjects: Parabolic system -- initial boundary value problem -- nonsmooth lateral boundary -- method of potentials -- boundary integral equations; 35K51 -- 35B65 -- 45D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2019.1698733
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: We consider the first initial boundary value problem for spatially one-dimensional parabolic second-order systems with Dini continuous coefficients in a semibounded domain with nonsmooth lateral boundary. We only require that the right-hand side of the boundary condition has continuous derivative of order 1/2 vanishing at t = 0. By the boundary integral equations method we construct a classical solution of this problem. The smoothness of the solution is studied.