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November/December 2009 On semilinear Cauchy problems with non-dense domain
Pierre Magal, Shigui Ruan
Adv. Differential Equations 14(11/12): 1041-1084 (November/December 2009).

Abstract

We are interested in studying semilinear Cauchy problems in which the closed linear operator is not Hille-Yosida and its domain is not densely defined. Using integrated semigroup theory, we study the positivity of solutions to the semilinear problem, the Lipschitz perturbation of the problem, differentiability of the solutions with respect to the state variable, time differentiability of the solutions, and the stability of equilibria. The obtained results can be used to study several types of differential equations, including delay differential equations, age-structure models in population dynamics, and evolution equations with nonlinear boundary conditions.

Citation

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Pierre Magal. Shigui Ruan. "On semilinear Cauchy problems with non-dense domain." Adv. Differential Equations 14 (11/12) 1041 - 1084, November/December 2009.

Information

Published: November/December 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1225.47042
MathSciNet: MR2560868

Subjects:
Primary: 35K57, 45D05, 47D06

Rights: Copyright © 2009 Khayyam Publishing, Inc.

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Vol.14 • No. 11/12 • November/December 2009
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