Computational Mathematics

Start control of positive solutions to Sobolev type equations

N. N. Solovyova, S. A. Zagrebina, G. A. Sviridyuk

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Using degenerate holomorphic groups of operators generated by linear continuous operators $L$ and $M$, a positive solution to a linear homogeneous Sobolev type equation is obtained; necessary and sufficient conditions for the positivity of these groups are found. Start control of positive solutions to the Showalter–Sidorov problem is investigated.

Keywords: start control problem, positive solutions, initial problem, abstract homogeneous Sobolev type equation.

UDC: 17.923+517.925.54

MSC: 43A35, 47B37

Received: 11.11.2025

Language: English

DOI: 10.14529/jcem250405