Research on the Properties of Solutions to Fourth-Order Pseudo-Parabolic Equations with Nonlocal Sources

Chunxiao Yang () and Wanqing Li
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Chunxiao Yang: School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
Wanqing Li: School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China

Mathematics, 2025, vol. 13, issue 15, 1-12

Abstract: This paper investigates the initial-boundary value problem for a fourth-order pseudo-parabolic equation with a nonlocal source: u t + Δ 2 u − Δ u t = u q − 1 u − 1 Ω ∫ Ω u q − 1 u d x . By employing the Galerkin method, the potential well method, and the construction of an energy functional, we establish threshold conditions for both the global existence and finite-time blow-up of solutions. Additionally, under the assumption of low initial energy J u 0 < d , an upper bound for the blow-up time is derived.

Keywords: pseudo-parabolic equation; global existence; potential well; blow-up time (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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