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

Pao, C. V.

doi:10.1090/S0002-9939-1977-0454362-7

Nonexistence of global solutions and bifurcation analysis for a boundary-value problem of parabolic type
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Proc. Amer. Math. Soc. 65 (1977), 245-251 Request permission

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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