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

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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)

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.

Suggested Citation

  • Chunxiao Yang & Wanqing Li, 2025. "Research on the Properties of Solutions to Fourth-Order Pseudo-Parabolic Equations with Nonlocal Sources," Mathematics, MDPI, vol. 13(15), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2415-:d:1711101
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