A priori estimates and existence of strong solutions for second order semi-linear parabolic systems

Vestnik of Samara University Natural Science Series 2026 Open access

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Authors: Sarvan T. Huseynov, R. A. Amanov, Narmin Amanova
DOI: 10.18287/2541-7525-2025-31-3-15-39
Cited by: 0

Abstract

This paper describes an interpolation method for obtaining a priori estimates for strong solutions of semilinear parabolic equations and systems with unbounded singularities in the right-hand side, provided that there is a first a priori estimate in the space of summable functions (see 10). Sufficient conditions for the existence of strong solution to the initial-boundary value problem for a semilinear parabolic system of second-order equations are obtained.

Fields of Study & Subjects

Differential Equations and Boundary Problems Nonlinear Partial Differential Equations Nonlinear Differential Equations Analysis

Publication details

Journal / source
Vestnik of Samara University Natural Science Series
Volume
31
Issue
3
Pages
15–39
Publication date
15 January 2026
Language
RU