Summary
This paper is concerned with the global solvability of the Cauchy problem for the abstract nonlinear equation
where A1, A2 are non-negative symmetric operators on an Hilbert space, while ϕ1, ϕ2 are locally Lipschitz continuous non-negative functions, in a Banach scale.
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D'Ancona, P. Global solution of the cauchy problem for a class of abstract nonlinear hyperbolic equations. Annali di Matematica pura ed applicata 151, 17–38 (1988). https://doi.org/10.1007/BF01762786
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DOI: https://doi.org/10.1007/BF01762786