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- W2892033576 abstract "In this paper we study microlocal regularity of a $mathcal{C}^2$ solution $u$ of the equation begin{equation*} u_t = f(x,t,u,u_x), end{equation*} where $f(x,t,zeta_0, zeta)$ is ultradifferentiable in the variables $(x,t)in mathbb{R}^{N} times mathbb{R}$ and holomorphic in the variables $(zeta_0,zeta) in mathbb{C} times mathbb{C}^{N}$. We proved that if $mathcal{C}^{mathcal{M}}$ is a regular Denjoy-Carleman class (including the quasianalytic case) then: begin{equation*} mathrm{WF}_mathcal{M} (u)subset mathrm{Char}(L^u), end{equation*} where $mathrm{WF}_mathcal{M}(u)$ is the Denjoy-Carleman wave-front set of $u$ and $mathrm{Char}(L^u)$ is the characteristic set of the linearized operator $L^u$: begin{equation*} L^u = dfrac{partial}{partial t} - sum_{j=1}^{N}frac{partial f}{partialzeta_j}(x,t,u,u_x)dfrac{partial}{partial x_j}. end{equation*}" @default.
- W2892033576 created "2018-09-27" @default.
- W2892033576 creator A5010072412 @default.
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- W2892033576 date "2018-09-18" @default.
- W2892033576 modified "2023-09-23" @default.
- W2892033576 title "Approximate solutions of vector fields and an application to Denjoy-Carleman regularity of solutions of a nonlinear PDE" @default.
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