ON THE BLOW-UP SOLUTIONS TO A FOURTH-ORDER PSEUDO-PARABOLIC EQUATION WITH GRADIENT NON-LINEARITY
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Abstract
In this note, the initial and periodic boundary value problem
was solved for the following fourth-order pseudo-parabolic equation
with gradient non-linearity and pseudo term
u_t − aΔu_t − Δu + Δ^2u = −∇ · (|∇u|^(p−2)∇u)
where a ≥ 0. Local existence-uniqueness result for mild solutions was
found for any initial data in L2(Ω). In addition, the existence of blowup
solutions was proved and a lower bound for the blow-up time was
obtained.
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Published
2024-07-22
How to Cite
Dilara Karslıoğlu. (2024). ON THE BLOW-UP SOLUTIONS TO A FOURTH-ORDER PSEUDO-PARABOLIC EQUATION WITH GRADIENT NON-LINEARITY. Results in Nonlinear Analysis, 7(3), 94–108. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/413
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