Blow-up for a non-degenerate non-local quasilinear wave equation on IR^N

Abstract

We study on the global existence, decay properties and blow-up results of the solution for the following non-degenerate nonlinear wave equation

where we have b ≥ 0, p ≥ 0, γ ≥ 1, δ > 0, φ(x) > 0 for all x∈ and a > 0.

Keywords:

• quasilinear hyperbolic equations
• global solution
• blow-up
• dissipation
• potential well
• concavity method
• unbounded domains
• Kirchhoff strings
• generalized sobolev spaces
• Weighted L^p Spaces

AMS Subject Classifications:

• 35A07
• 35B30
• 35B40
• 35B45
• 35L15
• 35L70
• 35L80

Acknowledgements

This work was co-funded by the European Social Fund (75%) and National Resources (25%) – Operational Program for Educational and Vocational Training II (EPEAEK II) and particularly by the PYTHAGORAS Program No. 68/831.