Variational approach for competitive systems with obstacles

S. Lenhart; S. Stojanovic; V. Protopopescu

doi:10.1016/0096-3003(91)90113-2

Variational approach for competitive systems with obstacles

S. Lenhart, S. Stojanovic, V. Protopopescu

Computational Sciences & Engineering Div

Research output: Contribution to journal › Article › peer-review

Abstract

We prove existence and uniqueness results for competitive systems consisting of two parabolic equations supplemented with positivity constraints. The coupling terms include local and nonlocal interaction terms. Monotone iteration schemes are used to obtain solutions in a variational approach. The solutions of the system are compared with the solution of a simplified ordinary differential system.

Original language	English
Pages (from-to)	65-83
Number of pages	19
Journal	Applied Mathematics and Computation
Volume	42
Issue number	1
DOIs	https://doi.org/10.1016/0096-3003(91)90113-2
State	Published - Mar 1991

Funding

This research has been partially sponsored by DARPA under contract 1868-A037-Al with Martin Marietta Energy Systems, Inc., which is under contract DE-AC05840R21400 with the U.S. Department of Energy. *Partially sponsored by the Defense Advanced Research Projects Agency. ‘Operated by the U.S. Department of Energy under Contract DE-AC05-840R21400 Martin Marietta Energy Systems, Inc.

Funders	Funder number
U.S. Department of Energy
Defense Advanced Research Projects Agency	DE-AC05-840R21400

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title = "Variational approach for competitive systems with obstacles",

abstract = "We prove existence and uniqueness results for competitive systems consisting of two parabolic equations supplemented with positivity constraints. The coupling terms include local and nonlocal interaction terms. Monotone iteration schemes are used to obtain solutions in a variational approach. The solutions of the system are compared with the solution of a simplified ordinary differential system.",

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AB - We prove existence and uniqueness results for competitive systems consisting of two parabolic equations supplemented with positivity constraints. The coupling terms include local and nonlocal interaction terms. Monotone iteration schemes are used to obtain solutions in a variational approach. The solutions of the system are compared with the solution of a simplified ordinary differential system.

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Variational approach for competitive systems with obstacles

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