2014/12/30 by Dmitri Finkelshtein, Finkelshtein, Dmitri
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35K90 #47D06 #60J80 #82C22 #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math-ph #math.FA #math.MP #math.PR #msc:35K90 #msc:47D06 #msc:60J80 #msc:82C22
paper · pdf · doi:10.48550/arxiv.1412.8628
arxiv created 2014/12/30 · openalex publication_date 2014/12/30 · arxiv updated 2014/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study existence, uniqueness, and a limiting behaviour of solutions to an abstract linear evolution equation in a scale of Banach spaces. The generator of the equation is a perturbation of the operator which satisfies the classical assumptions of Ovsyannikov's method by a generator of a C0-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [Math. Models Methods Appl. Sci., 25, 2, 2015, pp.343-370] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.