On a Semilinear Parabolic Problem with Four-Point Boundary Conditions

Marián Slodička
Additional contact information
Marián Slodička: Research Group NaM 2 , Department of Electronics and Information Systems, Ghent University, Krijgslaan 281, 9000 Ghent, Belgium

Mathematics, 2021, vol. 9, issue 5, 1-15

Abstract: This paper studies a semilinear parabolic equation in 1D along with nonlocal boundary conditions. The value at each boundary point is associated with the value at an interior point of the domain, which is known as a four-point boundary condition. First, the solvability of a steady-state problem is addressed and a constructive algorithm for finding a solution is proposed. Combining this schema with the semi-discretization in time, a constructive algorithm for approximation of a solution to a transient problem is developed. The well-posedness of the problem is shown using the semigroup theory in C -spaces. Numerical experiments support the theoretical algorithms.

Keywords: semilinear heat equation; four-point boundary conditions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/5/468/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/5/468/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:5:p:468-:d:505516

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().