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- W3095874341 abstract "In this paper we establish an invariant set bifurcation theory for the nonautonomous dynamical system $(va_lam,0)_{X,cH}$ generated by the evolution equation belabel{e0}u_t+Au=lam u+p(t,u),hs pin cH=cH[f(.,u)]ee on a Hilbert space $X$, where $A$ is a sectorial operator, $lam$ is the bifurcation parameter, $f(.,u):Rra X$ is translation compact, $f(t,0)equiv0$ and $cH[f]$ is the hull of $f(.,u)$. Denote by $va_lam:=va_lam(t,p)u$ the cocycle semiflow generated by the equation. Under some other assumptions on $f$, we show that as the parameter $lam$ crosses an eigenvalue $lam_0inR$ of $A$, the system bifurcates from $0$ to a nonautonomous invariant set $B_lam(.)$ on one-sided neighborhood of $lam_0$. Moreover, $$lim_{lamralam_0}H_{X^a}(B_lam(p),0)=0,hs pin P,$$ where $H_{X^a}(.,.)$ denotes the Hausdorff semidistance in $X^a$ (here $X^alpha$ ($ageq0$) defined below is the fractional power spaces associated with $A$). Our result is based on the pullback attractor bifurcation on the local central invariant manifolds $cM^lam_{loc}(.)$." @default.
- W3095874341 created "2020-11-09" @default.
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- W3095874341 date "2020-01-01" @default.
- W3095874341 modified "2023-09-26" @default.
- W3095874341 title "An invariant set bifurcation theory for nonautonomous nonlinear evolution equations" @default.
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- W3095874341 doi "https://doi.org/10.14232/ejqtde.2020.1.57" @default.
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