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2005, 2005(Special): 566-575. doi: 10.3934/proc.2005.2005.566

Monotone local semiflows with saddle-point dynamics and applications to semilinear diffusion equations

1. 

Dipartimento di Matematica, Università di Bari, via Orabona 4, 70125 Bari, Italy

2. 

Department of Mathematics and Statistics, Parker Hall, Auburn University, AL 36849-5310, United States

Received  September 2004 Revised  March 2005 Published  September 2005

Consider a monotone local semiflow in the positive cone of a strongly ordered Banach space, for which $0$ and $\infty$ are stable attractors, while all nontrivial equilibria are unstable. We prove that under suitable monotonicity, compactness, and smoothness assumptions, the two basins of attraction, $\Bz$ and $\Bi$, are separated by a Lipschitz manifold $\M$ of co-dimension one that forms the common boundary of $\Bz$ and $\Bi$. This abstract result is applied to a class of semilinear reaction-diffusion equations with superlinear, yet subcritical reaction terms.
Citation: Monica Lazzo, Paul G. Schmidt. Monotone local semiflows with saddle-point dynamics and applications to semilinear diffusion equations. Conference Publications, 2005, 2005 (Special) : 566-575. doi: 10.3934/proc.2005.2005.566
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