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- W3169175035 abstract "Abstract In this article, we study the observability (or equivalently, the controllability) of some subelliptic evolution equations depending on their step. This sheds light on the speed of propagation of these equations, notably in the ‘degenerated directions’ of the subelliptic structure. First, for any $gamma geq 1$ , we establish a resolvent estimate for the Baouendi–Grushin-type operator $Delta _{gamma }=partial _x^2+left lvert xright rvert ^{2gamma }partial _y^2$ , which has step $gamma +1$ . We then derive consequences for the observability of the Schrödinger-type equation $ipartial _tu-left (-Delta _{gamma }right )^{s}u=0$ , where $sin mathbb N$ . We identify three different cases: depending on the value of the ratio $(gamma +1)/s$ , observability may hold in arbitrarily small time or only for sufficiently large times or may even fail for any time. As a corollary of our resolvent estimate, we also obtain observability for heat-type equations $partial _tu+left (-Delta _{gamma }right )^su=0$ and establish a decay rate for the damped wave equation associated with $Delta _{gamma }$ ." @default.
- W3169175035 created "2021-06-22" @default.
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- W3169175035 date "2021-06-14" @default.
- W3169175035 modified "2023-10-02" @default.
- W3169175035 title "OBSERVABILITY OF BAOUENDI–GRUSHIN-TYPE EQUATIONS THROUGH RESOLVENT ESTIMATES" @default.
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- W3169175035 doi "https://doi.org/10.1017/s1474748021000207" @default.
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