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)).

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DOI:
https://doi.org/10.1090/S0002-9939-1975-0365265-9

Article copyright:
© Copyright 1975
American Mathematical Society