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Volume 19, Issue 2

# Blow-Up Results for Higher-Order Evolution Differential Inequalities in Exterior Domains

Mohamed Jleli
/ Mokhtar Kirane
• Pôle Sciences et Technologies, Université de La Rochelle, Avenue Michel Crépeau, 17031 La Rochelle, France; and NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
• Email
• Other articles by this author:
/ Bessem Samet
Published Online: 2019-02-02 | DOI: https://doi.org/10.1515/ans-2019-2040

## Abstract

We consider a higher-order evolution differential inequality in an exterior domain of ${ℝ}^{N}$, $N\ge 3$, with Dirichlet and Neumann boundary conditions. Using a unified approach, we obtain the critical exponents in the sense of Fujita for the considered problems. Moreover, the behavior of the solutions with respect to the initial data is discussed.

MSC 2010: 35B33; 35B44

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Revised: 2018-12-28

Accepted: 2019-01-20

Published Online: 2019-02-02

Published in Print: 2019-05-01

Mohamed Jleli and Bessem Samet extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No. RGP-237. The research of Mokhtar Kirane is supported by NAAM research group, University of King Abdulaziz, Jeddah.

Citation Information: Advanced Nonlinear Studies, Volume 19, Issue 2, Pages 375–390, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365,

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