A hyperbolic polyharmonic system in an exterior domain

Manal Alfulaij; Mohamed Jleli; Bessem Samet; Manal Alfulaij; Mohamed Jleli; Bessem Samet

doi:10.3934/math.2025123

AIMS Mathematics

2025, Volume 10, Issue 2: 2634-2651. doi: 10.3934/math.2025123

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A hyperbolic polyharmonic system in an exterior domain

Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia

Received: 15 September 2024 Revised: 17 December 2024 Accepted: 23 December 2024 Published: 14 February 2025
MSC : 35A01, 35B33, 35L55, 31B30

A nonlinear hyperbolic polyharmonic system in an exterior domain of $ \mathbb{R}^N $ is considered under inhomogeneous Navier-type boundary conditions. Using nonlinear capacity estimates specifically adapted to the polyharmonic operator $ (-\Delta)^m $, the geometry of the domain, and the boundary conditions, a sharp criterium for the nonexistence of weak solutions is obtained. Next, an optimal nonexistence result for the corresponding stationary problem is deduced.
- hyperbolic systems,
- polyharmonic operator,
- exterior domain,
- inhomogeneous Navier-type boundary conditions,
- weak solutions,
- nonexistence
Citation: Manal Alfulaij, Mohamed Jleli, Bessem Samet. A hyperbolic polyharmonic system in an exterior domain[J]. AIMS Mathematics, 2025, 10(2): 2634-2651. doi: 10.3934/math.2025123

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Abstract

A nonlinear hyperbolic polyharmonic system in an exterior domain of $ \mathbb{R}^N $ is considered under inhomogeneous Navier-type boundary conditions. Using nonlinear capacity estimates specifically adapted to the polyharmonic operator $ (-\Delta)^m $, the geometry of the domain, and the boundary conditions, a sharp criterium for the nonexistence of weak solutions is obtained. Next, an optimal nonexistence result for the corresponding stationary problem is deduced.

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