This research demonstrates the conditions for existence and blow-up of solutions in wave systems with damping and sources.
In this paper, we consider coupled nonlinear wave equations with degenerate damping and source terms and prove several results on potential well solutions via careful analysis involving the Nehari manifold. We prove the global existence of the unique weak solution with initial data from the stable part of the potential well. Whereas the solutions blow up in finite time with positive initial energy in the unstable set if the source terms are stronger than both damping terms.
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Li et al. (2026) studied this question.
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