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Mathematics
Volume 13
Issue 15
10.3390/math13152415
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Article

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

by
Chunxiao Yang
* and
Wanqing Li
School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(15), 2415; https://doi.org/10.3390/math13152415 (registering DOI)
Submission received: 12 June 2025 / Revised: 15 July 2025 / Accepted: 20 July 2025 / Published: 27 July 2025
Versions Notes

Abstract

This paper investigates the initial-boundary value problem for a fourth-order pseudo-parabolic equation with a nonlocal source: ut+Δ2u−Δut=uq−1u−1Ω∫Ωuq−1udx . 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 Ju0<d, an upper bound for the blow-up time is derived.
Keywords: pseudo-parabolic equation; global existence; potential well; blow-up time pseudo-parabolic equation; global existence; potential well; blow-up time

Share and Cite

MDPI and ACS Style

Yang, C.; Li, W. Research on the Properties of Solutions to Fourth-Order Pseudo-Parabolic Equations with Nonlocal Sources. Mathematics 2025, 13, 2415. https://doi.org/10.3390/math13152415

AMA Style

Yang C, Li W. Research on the Properties of Solutions to Fourth-Order Pseudo-Parabolic Equations with Nonlocal Sources. Mathematics. 2025; 13(15):2415. https://doi.org/10.3390/math13152415

Chicago/Turabian Style

Yang, Chunxiao, and Wanqing Li. 2025. "Research on the Properties of Solutions to Fourth-Order Pseudo-Parabolic Equations with Nonlocal Sources" Mathematics 13, no. 15: 2415. https://doi.org/10.3390/math13152415

APA Style

Yang, C., & Li, W. (2025). Research on the Properties of Solutions to Fourth-Order Pseudo-Parabolic Equations with Nonlocal Sources. Mathematics, 13(15), 2415. https://doi.org/10.3390/math13152415

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