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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References
Barthélemy, L.: Problème d'obstacle pour une équation quasi-linéaire du premier ordre, Ann. Fac. Sc. Toulous. IX(2), (1988), 137–159.
Barthélemy, L., and Bénilan, Ph.: Sous-potentiels d'un opérateur nonlinéaire, Israel J. Math. 61(1), (1988), 85–111.
Bénilan, Ph.: Equations d'evolution dans un espace de Banach quelconque et applications, Thèse Orsay (1972).
Bénilan, Ph., Crandall, M. G., and Pazy, A.: Evolution Equations Governed by Accretive Operators, book in preparation.
Bénilan, Ph., Crandall, M. G., and Pazy, A.: ‘Bonnes solutions’ d'un problème d'évolution semi-linéaire, C.R.Ac. Sc. Paris 306(1), (1988), 527–530.
Crandall, M. G.: The semigroup approach to first order quasilinear equations in several space variables, Israel J. Math. 12 (1972), 108–122.
Crandall, M. G.: Semidifferentials, quadratic forms and fully nonlinear elliptic equations of second order, to appear.
Crandall, M. G., and Lions, P. L.: Viscosity solutions of Hamilton Jacobi equation. Trans. Am. Math. Soc. 277 (1983), 1–42.
Kruskov, S. N.: First order quasilinear equation in several independant variables, Math. U.R.S.S. Sb. 10 (1970), 217–243.
Lions, P. L.: Generalized Solutions of Hamilton Jacobi Equations, Pitman (1984).
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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