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Subsolutions for abstract evolution equations

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Abstract

We study different notions of subsolutions for an abstract evolution equation du/dt+Au∋f where A is an m-accretive nonlinear operation in an ordered Banach space X with order-preserving resolvents. A first notion is related to the operator d/dt+A in the ordered Banach space L 1(0, T; X); a second one uses the evolution equation du/dt+A → u∋f where A →:x→{y;z≤y for some z∋Ax}; other notions are also considered.

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  1. Equipe de Mathématiques de Besançon, U.A. C.N.R.S. 741, Université de Franche Compté, 25030, Besançon Cedex, France

    Louise Barthélemy & Philippe Bénilan

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  1. Louise Barthélemy
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  2. Philippe Bénilan
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Barthélemy, L., Bénilan, P. Subsolutions for abstract evolution equations. Potential Anal 1, 93–113 (1992). https://doi.org/10.1007/BF00249788

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  • DOI: https://doi.org/10.1007/BF00249788

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