Nonlinear perturbations of evolution systems in scales of Banach spaces

Friesen M, Kutovyi O (2020)
Nonlinearity 33(11): 6134-6156.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Friesen, Martin; Kutovyi, OleksandrUniBi
Abstract / Bemerkung
A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem du(t)/dt = A(t)u(t) + B(u(t),t), u(0)=x in a scale of Banach spaces. Here A(t) is the generator of an evolution system acting in a scale of Banach spaces and B(u,t) obeys an Ovcyannikov-type bound. Continuous dependence of the solution with respect to A(t), B(u,t) and x is proved. The results are applied to the Kimura-Maruyama equation for the mutation-selection balance model. This yields a new insight in the construction and uniqueness question for nonlinear Fokker-Planck equations related with interacting particle systems in the continuum.
Stichworte
Cauchy-Kovalevskaya; nonlinear Fokker-Planck equation; nonlinear; evolution equation; Kimura-Maruyama; scale of Banach spaces
Erscheinungsjahr
2020
Zeitschriftentitel
Nonlinearity
Band
33
Ausgabe
11
Seite(n)
6134-6156
ISSN
0951-7715
eISSN
1361-6544
Page URI
https://pub.uni-bielefeld.de/record/2946747

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Friesen M, Kutovyi O. Nonlinear perturbations of evolution systems in scales of Banach spaces. Nonlinearity. 2020;33(11):6134-6156.
Friesen, M., & Kutovyi, O. (2020). Nonlinear perturbations of evolution systems in scales of Banach spaces. Nonlinearity, 33(11), 6134-6156. doi:10.1088/1361-6544/ab9dc9
Friesen, M., and Kutovyi, O. (2020). Nonlinear perturbations of evolution systems in scales of Banach spaces. Nonlinearity 33, 6134-6156.
Friesen, M., & Kutovyi, O., 2020. Nonlinear perturbations of evolution systems in scales of Banach spaces. Nonlinearity, 33(11), p 6134-6156.
M. Friesen and O. Kutovyi, “Nonlinear perturbations of evolution systems in scales of Banach spaces”, Nonlinearity, vol. 33, 2020, pp. 6134-6156.
Friesen, M., Kutovyi, O.: Nonlinear perturbations of evolution systems in scales of Banach spaces. Nonlinearity. 33, 6134-6156 (2020).
Friesen, Martin, and Kutovyi, Oleksandr. “Nonlinear perturbations of evolution systems in scales of Banach spaces”. Nonlinearity 33.11 (2020): 6134-6156.

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