Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
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.

References [Enhancements On Off] (What's this?)

  • [1] 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).
  • [2] H. A. Levine, Some nonexistence and instability theorems for formally parabolic equations of the form $ P{u_t} = - A(u) + \mathfrak{F}(u)$, Arch. Rational Mech. Anal. 51 (1973), 371-386. MR 0348216 (50:714)
  • [3] -, Instability and nonexistence of global solutions to nonlinear wave equations of the form $ P{u_{tt}} = - Au + \mathfrak{F}(u)$, Trans. Amer. Math. Soc. 192 (1974), 1-22. MR 0344697 (49:9436)
  • [4] H. A. Levine and L. E. Payne, Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, J. Differential Equations (to appear). MR 0470481 (57:10235)

Similar Articles

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

American Mathematical Society