Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints
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- by H. A. Levine and L. E. Payne PDF
- Proc. Amer. Math. Soc. 46 (1974), 277-284 Request permission
Abstract:
The present work extends previous results of the authors [4] on nonexistence of solutions of classes of second order equations subject to certain nonlinear boundary constraints and appropriate hypotheses on the data. Similar results are derived here for more general classes of higher order equations.References
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R. A. Knops, H. A. Levine and L. E. Payne, Nonexistence, instability and growth theorems for solutions to an abstract nonlinear equation with applications in elastodynamics Arch. Rational Mech. Anal. (to appear).
- Howard A. Levine, Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $Pu_{t}=-Au+{\scr F}(u)$, Arch. Rational Mech. Anal. 51 (1973), 371β386. MR 348216, DOI 10.1007/BF00263041
- 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 and Lawrence E. Payne, Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, J. Differential Equations 16 (1974), 319β334. MR 470481, DOI 10.1016/0022-0396(74)90018-7
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 277-284
- MSC: Primary 35G30
- DOI: https://doi.org/10.1090/S0002-9939-1974-0364841-6
- MathSciNet review: 0364841