Work

Well-posedness, blow up and asymptotic stability for fractional pseudo-parabolic equation involving memory and logarithmic terms

Year: 2025

Type: article

Abstract: Herein, we investigate the fractional pseudo-parabolic equation incorporating memory effect and logarithmic term $ \eta_{t}+(-\Delta)^s \eta+(-\Delta)^s \eta_{t} = \int_{0}^{t}k(t-\lambda)(-\Delta)^{s}\eta(\lambda)\,d\lambda+|\eta|^{r-2}\eta\ln|\eta| $ subject to Dirichlet boundary condition across various initial energy levels. To begin with, the local existence and uniqueness of weak solutions are rigorously established at any initial energy level via Galerkin approximation and contraction mapping principle. In addition, through the effective combination of Galerkin approximation, modified potential well theory, perturbed energy method and convexity theory etc, we explore the global existence and uniqueness, exponential and polynomial energy decay, as well as finite time blow up phenomena under low initial energy and critical initial energy levels.

Source: Discrete and Continuous Dynamical Systems - S

DOI: 10.3934/dcdss.2025111

Authors: Huafei Di, Yi Qiu, Xiaoming Peng

Institutions: Guangzhou University, Guangdong University Of Finances and Economics

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Basic and Applied Basic Research Foundation of Guangdong Province

Awards: G3849926402, G7574221095