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)

 

 

Nonexistence of global solutions and bifurcation analysis for a boundary-value problem of parabolic type


Author: C. V. Pao
Journal: Proc. Amer. Math. Soc. 65 (1977), 245-251
MSC: Primary 35K60
DOI: https://doi.org/10.1090/S0002-9939-1977-0454362-7
MathSciNet review: 0454362
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to present a bifurcation analysis on the existence of the nonexistence of a global solution for a semilinear parabolic equation and to characterize the local stability and the instability of the corresponding steady-state solutions. The bifurcation result can be described either by a parameter $ \lambda $ for a fixed spatial domain $ \Omega $ or by varying $ \Omega $ for a fixed $ \lambda $. The stability analysis gives a result which can be used to determine the stability or instability problem when the system possesses nonintersecting multiple steady-state solutions.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 35K60

Retrieve articles in all journals with MSC: 35K60


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0454362-7
Keywords: Nonexistence of global solution, parabolic equation, local stability and instability, bifurcation analysis
Article copyright: © Copyright 1977 American Mathematical Society