Dirichlet problem for parabolic systems with Dini continuous coefficients

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.

Keywords:

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

2010 Mathematics Subject Classifications:

• 35K51
• 35B65
• 45D05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was funded by Russian Science Foundation project no. 19-11-00033.