In this paper we provide sufficient conditions which ensure that the nonlinear equation d y(t) = Ay(t) d t+ σ(y(t)) d x(t) , t∈ (0 , T] , with y(0) = ψ and A being an unbounded operator, admits a unique mild solution such that y(t) ∈ D(A) for any t∈ (0 , T] , and we compute the blow-up rate of the norm of y(t) as t→ 0 +. We stress that the regularity of y is independent of the smoothness of the initial datum ψ, which in general does not belong to D(A). As a consequence we get an integral representation of the mild solution y which allows us to prove a chain rule formula for smooth functions of y.

Addona, D., Lorenzi, L., Tessitore, G. (2022). Regularity results for nonlinear Young equations and applications. JOURNAL OF EVOLUTION EQUATIONS, 22(1) [10.1007/s00028-022-00757-y].

Regularity results for nonlinear Young equations and applications

Tessitore G.
2022

Abstract

In this paper we provide sufficient conditions which ensure that the nonlinear equation d y(t) = Ay(t) d t+ σ(y(t)) d x(t) , t∈ (0 , T] , with y(0) = ψ and A being an unbounded operator, admits a unique mild solution such that y(t) ∈ D(A) for any t∈ (0 , T] , and we compute the blow-up rate of the norm of y(t) as t→ 0 +. We stress that the regularity of y is independent of the smoothness of the initial datum ψ, which in general does not belong to D(A). As a consequence we get an integral representation of the mild solution y which allows us to prove a chain rule formula for smooth functions of y.
Articolo in rivista - Articolo scientifico
Integral representation formula; Invariance property; Mild solutions and their smoothness; Nonlinear Young equations; Semigroups of bounded operators;
English
Addona, D., Lorenzi, L., Tessitore, G. (2022). Regularity results for nonlinear Young equations and applications. JOURNAL OF EVOLUTION EQUATIONS, 22(1) [10.1007/s00028-022-00757-y].
Addona, D; Lorenzi, L; Tessitore, G
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/359198
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