Critically and degenerately damped systems of nonlinear wave equations with source terms

Abstract

This article is concerned with the global well-posedness of the critically and degenerately damped system of nonlinear wave equations

in a bounded domain Ω ⊂ ℝ ⁿ , n = 1, 2, 3, with Dirichlét boundary conditions. The nonlinearities f ₁(u, v) and f ₂(u, v) act as a strong source in the system. Under some restriction on the parameters in the system we obtain several results concerning the existence of local solutions, global solutions, uniqueness and the blow up in finite time.

Keywords:

• wave equations
• damping and source terms
• weak solutions
• blow-up of solutions
• energy identity

AMS Subject Classifications::

• Primary 35L05
• 35L20
• Secondary 58G16

Acknowledgements

We would like to express our gratitude to anonymous referees whose valuable comments and suggestions helped improve the clarity and quality of this article.