Around Ovsyannikov's method
DOI:
Keywords:
Ovsyannikov’s method, scale of spaces, evolution equations, birth-and-deathdynamics, Vlasov scaling, kinetic equationAbstract
We study existence, uniqueness, and a limiting behavior 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 $C_0$-semigroup acting in each of the spaces of the scale. The results are (slightly modified) abstract version of those considered in [10] for a particular equation. An application to a birth-and-death stochastic dynamics in the continuum is considered.References
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