On Global Solvability for Some Degenerate Dissipative Nonlinear Kirchhoff Strings

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Consider the initial boundary value problem for degenerate dissipative wave equations of Kirchhoff type with attractive force terms.We are interested in the case of 0 < γ < 1 for the degeneracy of nonlinear term Φ(r) = rγ. We prove the global solvability problem, provided that the initial data belong to the potential well and satisfy a suitable smallness condition. Moreover, we derive optimal decay estimates of the solutions.

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