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Received May 15, 2021; Accepted September 1, 2021; Published October 1, 2021
Abstract. This paper addresses the well-posedness of nonautonomous Cauchy problems by using strongly continuous quasi-semigroups (-quasi-semigroups) on Banach spaces. Necessary and sufficient conditions for the nonautonomous Cauchy problem to be well-posed are that is the infinitesimal generator of a -quasi-semigroup. This paper also verifies the sufficiency for an operator to be the infinitesimal generator of a -quasi semigroup. A simple application in predicting that the persistence or extinction of a population growth model with diffusion and intrinsic growth rate are time-dependent is considered.
How to Cite this Article:
S. Sutrima, M. Mardiyana, R. Setiyowati, R. Respatiwulan, A new approach on the well-posedness of nonautonomous Cauchy problems: An application in population growth, Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 29, pp. 1-15.