Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms
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This article concerns the blow-up and asymptotic stability of weak solutions to the wave equation
utt - Δu + |u|kj′(ut) = |u|p-1u in Ω x (0, T),
where p > 1 and j′ denotes the derivative of a C1 convex and real value function j. We prove that every weak solution is asymptotically stability, for every m is such that 0 < m < 1, p < k + m and the initial energy is small; the solutions blow up in finite time, whenever p > k + m and the initial data is positive, but appropriately bounded.
CitationHu, Q., & Zhang, H. (2007). Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms. Electronic Journal of Differential Equations, 2007(76), pp. 1-10.
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