Asymptotic Analysis and Blow-Up of Solution for a q -Kirchhoff-Type Equation with Nonlinear Boundary Damping and Source Terms with Variable Exponents

Nouri Boumaza, Billel Gheraibia, Zayd Hajjej, Hongwei Zhang and Said Mesloub ()
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Nouri Boumaza: Department of Mathematics, Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria
Billel Gheraibia: Laboratory of Mathematics, Informatics and Systems (LAMIS), Echahid Cheikh Larbi Tebessi University, Tebessa 12000, Algeria
Zayd Hajjej: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Hongwei Zhang: Department of Mathematics, Henan University of Technology, Zhengzhou 450001, China
Said Mesloub: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Mathematics, 2025, vol. 13, issue 22, 1-18

Abstract: In this study, we examine a q -Kirchhoff-type equation defined on a bounded domain, incorporating nonlinear boundary damping and source terms with variable exponents. Assuming appropriate conditions on the initial data and the variable exponent functions, we establish the global existence of solutions. Subsequently, we derive a general decay estimate for these solutions. Lastly, we demonstrate that solutions with negative initial energy exhibit finite-time blow-up.

Keywords: q -Kirchhoff type equation; variable exponents; nonlinear boundary conditions; global existence; general decay; blow-up (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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