Further global nonexistence theorems for abstract nonlinear wave equations
HTML articles powered by AMS MathViewer
- by Brian Straughan PDF
- Proc. Amer. Math. Soc. 48 (1975), 381-390 Request permission
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 βescape timeβ are given. A similar nonexistence theorem is also proved for a nonlinear wave equation with dissipation (see equations (3.1)).References
- Robert T. Glassey, Blow-up theorems for nonlinear wave equations, Math. Z. 132 (1973), 183β203. MR 340799, DOI 10.1007/BF01213863
- R. J. Knops, H. A. Levine, and L. E. Payne, Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elastodynamics, Arch. Rational Mech. Anal. 55 (1974), 52β72. MR 364839, DOI 10.1007/BF00282433
- Howard A. Levine, Instability and nonexistence of global solutions to nonlinear wave equations of the form $Pu_{tt}=-Au+{\cal F}(u)$, Trans. Amer. Math. Soc. 192 (1974), 1β21. MR 344697, DOI 10.1090/S0002-9947-1974-0344697-2
- Howard A. Levine, Some additional remarks on the nonexistence of global solutions to nonlinear wave equations, SIAM J. Math. Anal. 5 (1974), 138β146. MR 399682, DOI 10.1137/0505015
- Howard A. Levine, A note on a nonexistence theorem for nonlinear wave equations, SIAM J. Math. Anal. 5 (1974), 644β648. MR 361960, DOI 10.1137/0505064 β, On the nonexistence of global solutions to a nonlinear Euler-Poisson-Darboux equation, J. Math. Anal. Appl. (in print).
- Masayoshi Tsutsumi, On solutions of semilinear differential equations in a Hilbert space, Math. Japon. 17 (1972), 173β193. MR 355247
Additional Information
- © Copyright 1975 American Mathematical Society
- 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