Bitsadze–Samarskii problem for parabolic systems with Dini continuous coefficients

ABSTRACT

We consider a nonlocal initial-boundary value problem of the Bitsadze–Samarskii type for spatially one-dimensional parabolic second-order systems with Dini continuous coefficients in a domain with nonsmooth lateral boundaries. By the boundary integral equations method we construct a classical solution of this problem. The smoothness of the solution is studied.

COMMUNICATED BY:

• A. Soldatov

Keywords:

• Parabolic system
• initial-boundary value problem
• nonsmooth lateral boundary
• method of potentials
• boundary integral equations

AMS SUBJECT Classifications:

• 35K51
• 35B65
• 45D05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

M.F. Cherepova acknowledges the support of the Russian Science Foundation, project no. 14-11-00306.