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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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