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Proceedings of the American Mathematical Society

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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
MathSciNet review: 0454362
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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.

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Keywords: Nonexistence of global solution, parabolic equation, local stability and instability, bifurcation analysis
Article copyright: © Copyright 1977 American Mathematical Society

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