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Further global nonexistence theorems for abstract nonlinear wave equations


Author: Brian Straughan
Journal: Proc. Amer. Math. Soc. 48 (1975), 381-390
MSC: Primary 47H15; Secondary 35R20
DOI: https://doi.org/10.1090/S0002-9939-1975-0365265-9
MathSciNet review: 0365265
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Abstract: It is shown that solutions to a nonlinear abstract wave equation (see equations (2.1)) under specified initial data cannot exist for all time. Precise estimates for the growth of solutions and the 'escape time' are given. A similar nonexistence theorem is also proved for a nonlinear wave equation with dissipation (see equations (3.1)).


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0365265-9
Article copyright: © Copyright 1975 American Mathematical Society

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