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Equilibria, connecting orbits and a priori bounds for semilinear parabolic equations with nonlinear boundary conditions


Chipot, M; Quittner, P (2004). Equilibria, connecting orbits and a priori bounds for semilinear parabolic equations with nonlinear boundary conditions. Journal of Dynamics and Differential Equations, 16(1):91-138.

Abstract

We consider a semilinear parabolic equation with a nonlinear non-dissipative boundary condition. In the one-dimensional case we describe bifurcation diagrams for positive and sign-changing equilibria and connecting orbits between these equilibria. We also show that the number of sign-changing stationary solutions strongly depends on the spatial dimension. The results are based on new a priori estimates of global solutions.

Abstract

We consider a semilinear parabolic equation with a nonlinear non-dissipative boundary condition. In the one-dimensional case we describe bifurcation diagrams for positive and sign-changing equilibria and connecting orbits between these equilibria. We also show that the number of sign-changing stationary solutions strongly depends on the spatial dimension. The results are based on new a priori estimates of global solutions.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:emilinear parabolic equation - nonlinear boundary condition - blow-up - equilibrium - heteroclinic orbit - a priori estimates
Language:English
Date:2004
Deposited On:10 Jun 2010 12:56
Last Modified:05 Apr 2016 13:24
Publisher:Springer
ISSN:1040-7294
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1023/B:JODY.0000041282.14930.7a
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2093837

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