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September 10, 2025Open Access

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

Key Points

Global existence and finite-time blow-up conditions are established for a fourth-order equation.
The study derives an upper bound for blow-up time, informed by low initial energy thresholds.
Threshold conditions were determined through the application of the Galerkin method and energy functional.
Results suggest critical insights for resolving initial-boundary value problems under nonlocal influences.

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.

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

Key Points

Abstract

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