On a nonclassical problem for the heat equation and the Feller semigroup generated by it

Array

Authors

  • B.I. Kopytko Czestochowa University of Technology, 69 Dabrowskiego str., 42-201, Czestochowa, Poland https://orcid.org/0000-0003-3793-4838
  • A.F. Novosyadlo Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine

DOI:

https://doi.org/10.15330/cmp.12.2.297-310

Keywords:

parabolic potential, boundary integral equation method, Feller semigroup, nonlocal boundary condition

Abstract

The initial boundary value problem for the equation of heat conductivity with the Wenzel conjugation condition is studied. It does not fit into the general theory of parabolic initial boundary value problems and belongs to the class of conditionally correct ones. In space of bounded continuous functions by the method of boundary integral equations its classical solvability under some conditions is established. In addition, it is proved that the obtained solution is a Feller semigroup, which represents some homogeneous generalized diffusion process in the area considered here.

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Published

2020-11-03

How to Cite

(1)
Kopytko, B.; Novosyadlo, A. On a Nonclassical Problem for the Heat Equation and the Feller Semigroup Generated by It: Array. Carpathian Math. Publ. 2020, 12, 297-310.

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Section

Scientific articles