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Further Global Nonexistence Theorems for Abstract Nonlinear Wave Equations
Proceedings of the American Mathematical Society
Vol. 48, No. 2 (Apr., 1975), pp. 381-390
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040270
Page Count: 10
You can always find the topics here!Topics: Wave equations, Nonexistence, Mathematical theorems, Hilbert spaces, Mathematical functions
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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)).
Proceedings of the American Mathematical Society © 1975 American Mathematical Society