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Further Global Nonexistence Theorems for Abstract Nonlinear Wave Equations

Brian Straughan
Proceedings of the American Mathematical Society
Vol. 48, No. 2 (Apr., 1975), pp. 381-390
DOI: 10.2307/2040270
Stable URL: http://www.jstor.org/stable/2040270
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Further Global Nonexistence Theorems for Abstract Nonlinear Wave Equations
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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)).

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