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Global Well-posedness and Asymptotic Analysis of a Damped Nonlinear Wave Equation with a Codimension-One Constraint
We prove the global existence and uniqueness of strong solutions to a constrained version of the damped nonlinear wave equation $$ \vartheta_{tt}+γ\vartheta_t-Δ\vartheta+|\vartheta|^{p-2}\vartheta=0 $$ on a smooth bounded domain $\varOmega\subset\mathbb{R}^d$, where the evolution is projected onto
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