On Initial-boundary Value Problems for Parabolic Systems in a Semi-bounded Plane Domain With General Boundary Conditions
Year: 2024
Type: article
Abstract: The paper considers initial boundary value problems for homogeneous parabolic systems with Dini-continuous coefficients under zero initial conditions in a semi-bounded plane domain with a non- smooth lateral boundary that admits the presence of ”beaks”on which boundary conditions of a general type with variable coefficients are specified. Using the method of boundary integral equations, a theorem is proved on the unique classical solvability of such problems in the space of functions that are continuous and bounded together with their first-order spatial derivative in the closure of the domain. A representation of the solutions obtained is given in the form of vector single layer potentials.
Author: S. I Sakharov
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4405611075