Some nonexistence theorems for initial-boundary value problems with nonlinear boundary constraints
Authors:
H. A. Levine and L. E. Payne
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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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.
-
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 https://doi.org/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 https://doi.org/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 https://doi.org/10.1016/0022-0396%2874%2990018-7
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35G30
Retrieve articles in all journals with MSC: 35G30
Additional Information
Keywords:
Nonexistence theorems,
initial-boundary value problems,
nonlinear boundary constraints,
concavity methods,
differential inequalities,
finite escape time
Article copyright:
© Copyright 1974
American Mathematical Society